|
2008年10月
|
| 报告题目： |
On
time change theory for symmetric Markov processes (I) |
| 报
告 人： |
Prof.
M. Fukushima (Professor Emeritus Osaka University, Japan) |
| 时间地点： |
2008年10月29日（星期三）下午2:30-3:30 思源楼703 |
| 摘 要： |
. |
| 报告题目： |
Talagrand和对数Sobolev不等式 |
| 报
告 人： |
吴黎明 教授,法国Blaise Pascal大学 |
| 时间地点： |
2009年7月30日（星期四） 下午4:00-5:00
思源楼703室 |
| 摘 要： |
我们通过实用的Lyapunov函数条件导出Talagrand不等式，并且在一定曲率条件下导出对数Sobolev不等式。最优运输映射起重要作用。 |
|
|
| 报告题目： |
On
the Path to Extinction |
| 报
告 人： |
Prof.
Peter Jagers (Chalmers University of Technology, Sweden ) |
| 时间地点： |
2008年10月27日（星期一）下午3:00-4:00 思源楼703 |
| 摘 要： |
Populations
can die in many ways. Arguably the most basic is extinction
for intrinsic reasons, by stably insufficient, i.e. subcritical,
reproduction. We consider (moderately) large, subcritical general
branching processes, and ask what the time T to extinction is.
It turns out that T has two components, both carrying weight,
a deterministic part, proportional to the logarithm of initial
population size, and a random part, with an approximate Gumbel
distribution. Then we consider the path to extinction. How large
will the population be at time uT, 0<u<1? There is a beautiful
limiting form, for large initial populations, of this as a stochastic
process on the unit interval. For u close to one the approximation
is bad but in the case of Markov branching process we can describe
the last minutes before extinction. (Joint work with Fima Klebaner
and Serik Sagitov, published in the Proc Nat. Acad. of US (2007)
and J. Appl. Prob. (2007). |
|
|
| 报告题目： |
Applications
of a Markov mapping theorem |
| 报
告 人： |
Prof.
Thomas Kurtz (University of Wisconsin, USA ) |
| 时间地点： |
2008年10月20日（星期一）下午3:00-4:00 思源楼703 |
| 摘 要： |
Conditions
in terms of generators are given under which the image of a
solution of a martingale problem with values in one metric space
gives a solution of a martingale problem with values in the
image space. Applications of the general result will be discussed
including the equivalence between martingale problems and stochastic
differential equations, and uniqueness for stochastic partial
differential equations. |
|
|
|
2008年9月
|
| 报告题目： |
Asymptotic
regimes of the occupation scheme for multiplicative cascades
|
| 报
告 人： |
Dr.
Jean Bertoin (Université Pierre et Marie Curie (Paris VI) )
|
| 时间地点： |
2008年9月1日（星期一）下午3:40-4:40 思源楼703 |
| 摘 要： |
In
the classical occupancy scheme, one considers a fixed discrete
probability measure ${\bf p}=(p_i: {i\in{\cal I}})$ and throws
balls independently at random in boxes labeled by ${\cal I}$,
such that $p_i$ is the probability that a given ball falls into
the box $i$. In this lecture, we are interested in asymptotic
regimes of this scheme in the situation induced by a refining
sequence $({\bf p}(k): k\in\N)$ of random probability measures
which arise from some multiplicative cascade. Our motivation
comes from the study of the asymptotic behavior of certain fragmentation
chains. |
|
|
| 报告题目： |
The
continuous limit of large random planar maps |
| 报
告 人： |
Dr.
Jean-Francois Le Gall (Universite Paris XI and Institut universitaire
de France) |
| 时间地点： |
2008年9月1日（星期一）下午2:30-3:30 思源楼703 |
| 摘 要： |
Planar
maps are graphs embedded in the plane, considered up to continuous
deformation. They have been studied extensively in combinatorics,
and they also have significant geometrical applications. Random
planar maps have been used in theoretical physics, where they
serve as models of random geometry. Our goal is to discuss the
convergence in distribution of rescaled random planar maps viewed
as random metric spaces. More precisely, we consider a random
planar map M(n) which is uniformly distributed over the set
of all planar maps with n vertices in a certain class. We equip
the set of vertices of M(n) with the graph distance rescaled
by the factor n to the power -1/4. We then discuss the convergence
in distribution of the resulting random metric spaces as n tends
to infinity, in the sense of the Gromov-Hausdorff distance between
compact metric spaces. This problem was stated by Oded Schramm
in his 2006 ICM paper, in the special case of triangulations.
In the case of bipartite planar maps, we first establish a compactness
result showing that a limit exists along a suitable subsequence.
We then prove that this limit can be written as a quotient space
of the so-called Continuum Random Tree (CRT) for an equivalence
relation which has a simple definition in terms of Brownian
labels attached to the vertices of the CRT. This limiting random
metric space, which is called the Brownian map, can be viewed
as a "Brownian surface" in the same sense as Brownian
motion is the limit of rescaled discrete paths. We show that
the Brownian map is almost surely homeomorphic to the two-dimensional
sphere, although it has Hausdorff dimension 4. Furthermore,
we are able to give a complete description of the geodesics
from a distinguished point (the root) of the Brownian map, and
in particular of those points which are connected by more than
one geodesic to the root. As a key tool, we use bijections between
planar maps and various classes of labeled trees. |
|
|
|
2008年7月
|
| 报告题目： |
Stein's
method of exchangeable pairs with application to the Curie-Weiss
Model |
| 报
告 人： |
Prof.
Qi-Man Shao (Hong Kong University of Science and Technology)
|
| 时间地点： |
2008年7月2日（星期三）下午3:00-4:00 思源楼1013 |
| 摘 要： |
|
|
|
|
2008年4月
|
| 报告题目： |
On
the existence of solutions for unidimensional BSDE's |
| 报
告 人： |
Prof.
Jean-Pierre Lepeltier (Universite du Maine, Le Mans, France)
|
| 时间地点： |
2008年4月15日（星期二）下午4:00-5:00 晨兴数学中心110 |
| 摘 要： |
|
|
|
| 报告题目： |
Markov
loops and fields |
| 报
告 人： |
Prof.
Yves Le Jan （巴黎南大学） |
| 时间地点： |
2008年4月14日（星期一）下午3:00-4:00 思源楼703室 |
| 摘 要： |
We
will investigate Poisson processes of Markov loops and the associated
occupation fields, which, in cetain cases are related to the
free field. Renormalisation problems will be adressed in the
case of Brownian loops. |
|
2008年3月
|
| 报告题目： |
树，随机游动，
聚合物 |
| 报
告 人： |
施展教授（巴黎第六大学） |
| 时间地点： |
2008年3月24日（星期一）下午3:00-4:00 思源楼703室 |
| 摘 要： |
演讲人简介：施展教授早年就读于中国科技大学（本科)和中科院应用数学研究所（研究生）,
1986年负笈法国巴黎，师从著名概率学家Marc Yor, 1990年获博士学位，1998年任巴黎第六大学概率论实验室（Laboratoire
de Probabilités et Modèles Aléatoires）教授至今。施展教授的研究范围包括布朗运动、随机游动、大偏差估计等随机过程的多个方面，详细情况请见其个人主页
http://www.proba.jussieu.fr/pageperso/zhan/. |
|
2007年12月
|
| 报告题目： |
A
survey of quantum stochastic calculus |
| 报
告 人： |
Prof.
Robin Hudson, Loughborough University, UK |
| 时间地点： |
2007年12月13日（星期四）下午4:00-5:00 思源楼703室 |
| 摘 要： |
Quantum
stochastic calculus originated as a noncommutative generalisation
of the Ito calculus of Brownian motion, motivated by the so-called
Wiener-Segal isomorphism between the L^2 space of Wiener space
and a Fock space. The Poisson process and other Levy processes
are naturally incorporated into the same formalism. Ito corrections
are related to quantum commutation relations. Generalisations
and some applications in physics and in finance will be discussed. |
|
|
| 报告题目： |
Quantum
constrained systems and quantum graphs |
| 报
告 人： |
Prof.
Gianfausto Dell'antonio,University Roma I and SISSA |
| 时间地点： |
2007年12月13日（星期四）下午3:00-4:00 思源楼703室 |
| 摘 要： |
In
this talk I will outline the theory of constrained systems in
Quantum Mechanics as a multiscale process. I shall give some
examples and use it as a framework for the study of the limit
Schroedinger equation on quantum graphs.
|
|
2007年11月
|
|
| 报告题目： |
Feynman-Kac
formula and ralated problem |
| 报
告 人： |
应坚刚
教授, 复旦大学数学学院 |
| 时间地点： |
2007年11月26日（星期一）下午3:00-4:00 思源楼712室 |
| 摘 要： |
|
|
2007年10月
|
| 报告题目： |
Stochastic
porous media and Dirichlet spaces |
| 报
告 人： |
Prof.
Byron Schmuland, University of Alberta, Canada |
| 时间地点： |
2007年10月22日（星期一）下午3:00-4:00 思源楼703室 |
| 摘 要： |
Recent
developments in solving stochastic porous media equations benefit
from the theory of Dirichlet forms. I show how some older results
on extended Dirichlet space help to put these equations in the
right context. |
|
2007年9月
|
| 报告题目： |
Insurance
Claims Modulated by a Hidden Marked Point Process |
| 报
告 人： |
Prof.
Robert J. Elliott, RBC Financial Group Professor of Finance,Haskayne
School of Business,University of Calgary, Canada |
| 时间地点： |
2007年9月24日（星期一）下午4:00-5:00 思源楼703室 |
| 摘 要： |
Recently
there has been interest in applying Markov modulated Poisson
processes to ruin theory. Such a model can incorporate the impact
states of the economy have on the surplus process. However,
the Markov chain is often not directly observable in practice.
We develop smoothing and filtering results when the hidden Markov
chain influences both the timing and size of insurance claims.
The parameters of the model are also estimated. |
|
|
| 报告题目： |
Ageing
in Meanfield Spin Glasses |
| 报
告 人： |
Prof.
Anton Bovier，德国Weierstrass Institute |
| 时间地点： |
2007年9月17日（星期一）下午3:00-4:00 思源楼703室 |
| 摘 要： |
.
|
|
2007年8月
|
| 报告题目： |
Probability
and Fourier Transforms with Only Real Zeros |
| 报
告 人： |
Prof.
Wenbo Li, University of Delaware |
| 时间地点： |
2007年8月6日（星期一）上午10:00-11:00 思源楼703室 |
| 摘 要： |
The
study of Fourier transforms with only real zeros has significant
impacts in combinatorics, analysis and probability. We will
provide several examples to demonstrate interplays with probability.
|
|
|
| 报告题目： |
On
Independence Tests Based on Large Sample Correlation Matrices |
| 报
告 人： |
Prof.
Qi-Man Shao, Hong Kong University of Science and Technology，University
of Oregon |
| 时间地点： |
2007年8月6日（星期一）上午9:00-10:00 思源楼703室 |
| 摘 要： |
Let
X1, · · · ,Xn be a random sample from a p-dimensional population
distribution. Assume that both p and n are large. To test whether
the p-variates of the population are independent, Jiang (2004)
uses the largest entry of the sample correlation matrix as a
test statistic and the limiting distribution is the extreme
distribution of type I. It is known that the rate of convergence
to this type of extreme distribution is typically slow, of order
of O(1/ log n). In this talk we will introduce a new test statistic
which also has an extreme limiting distribution of type I but
with a rate of convergence O((log n)3/n1/2). Other related problems
will also be discussed. This talk is based on a joint work with
W.D. Liu and Z.Y. Lin at Zhejiang University. |
|
2007年7月
|
| 报告题目： |
Poinacre
inequalities and Sobolev inequalities on differential forms
over complete Riemannian manifolds |
| 报
告 人： |
Prof.
Xiang-Dong Li, University of Toulouse III, France |
| 时间地点： |
2007年7月27日（星期五）下午4:00-5:00 思源楼712室 |
| 摘 要： |
In
this talk, I will present some of my recent work on Poincare
inequalities and Sobolev inequalities on differential forms
over complete Riemannian manifolds. As application, I present
some $L^p$-estimates and existence theorems of the De Rham equation
$d\omega=\alpha$ as well as some vanishing theorems of the $L^p$-cohomology
on complete Riemannian manifolds. |
|
|
| 报告题目： |
Schramm
Loewner Evolutions and Generalizations |
| 报
告 人： |
关庆扬
助理研究员, Institute of Applied Mathematics, CAS Department of Mathematics,Imperial
College London |
| 时间地点： |
2007年7月27日（星期五）下午3:00-4:00 思源楼712室 |
| 摘 要： |
Schramm
Loewner Evolutions (SLE) are new methods to study conformal
invariant curves or compact sets in two dimensional plane. In
this talk we first give an introduction of this excited subject.
Then we consider stochastic Loewner equation driven by more
general L\'evy processes which give increasing clusters with
trees-like structure. We show that the increasing clusters can
be generated by c\'adl\'ag curves. We also introduce a new class
of ordinary differential equations called $\alpha$-Loewner equation
and define $\alpha$-SLE. The corresponding clusters have $\alpha$-self-similarity.
We show the phase transition of $\alpha$-SLE at a critical coefficient
$\theta=\theta_0(\alpha)$ analogous to the $\kappa=4$ phase
transition in Brownian SLE. Finally we discuss the possibility
of SLE in high dimensional cases. |
|
|
| 报告题目： |
Potential
theory of subordinate Brownian motions |
| 报
告 人： |
宋仁明
教授, University of Illinois at Urbana-Champaign |
| 时间地点： |
2007年7月23日（星期一）下午3:00-4:00 思源楼712室 |
| 摘 要： |
In
this talk, I will give a survey of recent progress in the study
of potential theory of subordinate Brownian motions.
|
|
2007年6月
|
| 报告题目： |
Rounded
Data Analysis |
| 报
告 人： |
白志东院士, 东北师范大学 |
| 时间地点： |
2007年6月4日（星期一）下午3:00-4:00 思源楼712室 |
| 摘 要： |
Except categorical
data, all continuous data need to be rounded when they are
collected and recorded. The rounding errors definitely affect
the accuracy of statistical inferences. In old days, it was
not seriously treated because statistical problems are only
met for small samples. However, with the wide application
of advanced computers, statisticians are gradually facing
to deal with data of large sample with large dimension. This
forces our statisticians to pay serious attention to the rounding
errors. It has been found in the literature that the usual
t-test will reject the true null hypothesis with probability
near to 1 when the sample size is large enough. This shows
that we have to search new methodologies to deal with analysis
of data when the observations are rounded and the rounding
scale is large relatively to the sample size. In a series
of my recent research works, we proposed some new methods
to deal with the analysis of rounded data
.In this talk,
I will revisit an example discussed by Dempster and Rubin
in their 1982 JRSSB paper. We will show that Sheppard corrections
are superior to the BRB corrections only for their example
and generally not the case. Further, we propose a new method
to find consistent and asymptotically normal estimates in
rounded linear models. The new method is named as two-stage
estimation
.
|
|
2007年4月
|
| 报告题目： |
Quantum
Entanglement and Related Mathematics |
| 报
告 人： |
Prof.
Shao-Ming Fei, Bonn University,Capital Normal University |
| 时间地点： |
2007年4月12日（星期四）下午4:00-5:00 思源楼703室 |
| 摘 要： |
We
introduce some basic concepts and recent developments in the
theory of quantum entanglement used in quantum information processing
and computation, in particular, the measure of entanglement,
separability criteria, invariants and geometry of quantum states
under local unitary transformations. |
|
2007年1月
|
| 报告题目： |
Geometric
Stochastic Analysis on Path Spaces |
| 报
告 人： |
Prof.
K. David Elworthy , Mathematics Institute, Warwick University,
UK |
| 时间地点： |
2007年1月4日（星期四）下午4:00-5:00 思源楼703室 |
| 摘 要： |
An
approach to analysis on path spaces of Riemannian manifolds
is described. The spaces are furnished with 'Brownian motion'
measure which lies on continuous paths, though differentiation
is restricted to directions given by tangent paths of finite
energy. An introduction describes the background for paths on
Rm and Malliavin calculus. For manifold valued paths the approach
is to use 'It?o' maps of suitable stochastic differential equations
as charts. 'Suitability' involves the connection determined
by the stochastic differential equation. Some fundamental open
problems concerning the calculus and the resulting 'Laplacian'
are described. A theory for more general diffusion measures
is also briefly indicated. The same method is applied as an
approach to getting over the fundamental difficulty of defining
exterior differentiation as a closed operator, with success
for one and two forms leading to a Hodge-Kodaira operator and
decomposition for such forms. Finally there is a brief description
of some related results for loop spaces. |
|
2006年12月
|
| 报告题目： |
Hranack不等式的耦合方法 |
| 报
告 人： |
王凤雨 教授 , 北京师范大学 |
| 时间地点： |
2006年12月18日（星期一）下午4:00-5:00 思源楼703室 |
| 摘 要： |
.介绍使用耦合方法证明Harnack不等式的基本思想，
并应用于流形上具无下界曲率的扩散半群以及一类随机偏微分方程的研究。特别地，证明了一般随机porous medium 方程的几种超压缩性、强Feller性和热核估计等 |
|
2006年11月
|
| 报告题目： |
Expected
Length of Minimum Spanning Tree |
| 报
告 人： |
Prof.
Wenbo Li, University of Delaware, USA |
| 时间地点： |
2006年11月13日（星期一）下午4:00-5:00 晨兴数学中心110 |
| 摘 要： |
An
exact formula for the expected length of the minimum spanning
tree of a connected graph with independent and identical edge
distribution is given, which generalizes Steele's formula in
the uniform case. For complete graph, the difference of expected
lengths between exponential with rate one and uniform on the
interval (0,1) is shown to be positive and of rate zeta(3)/n..
This is a joint work with Xinyi Zhang . |
|
2006年10月
|
| 报告题目： |
Works
of 2006 Fields Medalists in Probability |
| 报
告 人： |
Prof.
Wenbo Li, University of Delaware, USA |
| 时间地点： |
2006年10月23日（星期一）下午4:00-5:00 晨兴数学中心110 |
| 摘 要： |
The
Fields Medals are the most important international prize in
the world of mathematics.They are awarded by the International
Mathematical Union (IMU) every four years at the ICM (International
Congress of Mathematicians).Between two and four Fields Medals
can be awarded at each ICM to only mathematicians below the
age of 40 in order to encourage future endeavor..They are typically
awarded for a body of work, rather than a single isolated achievement.
The winners of the Fields Medals awarded in ICM2006 are: Andrei
Okounkov, Grigori Perelman, Terence Tao, and Wendelin Werner.Their
works related to probability theory will be discussed in this
talk, which should be understandable for a wide audience.I hope
to convince the audience/students that they should learn as
much probability as possible.Without any double, probability
theory has became one of the most fascinating, fast growing
and main stream mathematics. |
|
2006年9月
|
| 报告题目： |
Local
stochastic differential geometry: feeling the shape of a manifold
with Brownian motion |
| 报
告 人： |
Prof.
Mark Pinsky, Department of Mathematics, Northwestern University,
USA |
| 时间地点： |
2006年9月11日（星期一）下午3:00-4:00 思源楼703 |
| 摘 要： |
.
|
|
2006年7月
|
| 报告题目： |
Relativistic
Diffusions and Schwarzschild Geometry |
| 报
告 人： |
Prof.
Jacques FRANCHI（University of Louis Pasteur, Strasbourg, France） |
| 时间地点： |
2006年7月21日（星期五）下午3:00-4:00 思源楼703 |
| 摘 要： |
This
talk is based on a joint work with Yves LeJan. We shall develop
Ito calculus for relativistic diffusions. |
|
|
| 报告题目： |
Limiting
Theorems Associated with Poisson-Dirichlet Distributions |
| 报
告 人： |
Prof.
Shui Feng（Dept. of Mathematics & Statistics, McMaster University,
Canada） |
| 时间地点： |
2006年7月3日（星期一）下午3:00-4:00 思源楼703 |
| 摘 要： |
Some
limiting theorems will be discussed for Poisson-Dirichlet distribution
and its random sample. These results are motivated for the understanding
of the exact meaning of large mutation rate. |
|
2006年6月
|
| 报告题目： |
Gaussian
Inequalities and Conjectures |
| 报
告 人： |
Prof.
Wenbo Li (University of Delaware, USA） |
| 时间地点： |
2006年6月12日（星期一）下午3:00-4:00 思源楼712 |
| 摘 要： |
..
|
|
|
| 报告题目： |
Spectral
Measure of Large Hankel, Markov and Toeplitz Matrices |
| 报
告 人： |
Tiefeng
Jiang (Associate Professor,School of Statistics, University
of Minnesota, USA |
| 时间地点： |
2006年6月12日（星期一）下午3:00-4:00 思源楼712 |
| 摘 要： |
We
study the limiting spectral measure of large symmetric random
matrices. This includes the asymptotic behavior of properly
scaled eigenvalues of Hankel, Markov and Toeplitz matrices.
This solves three unsolved random matrix problems. It is the
joint work with W. Bryc and A. Dembo. |
|
2006年5月
|
| 报告题目： |
Intrinsic
ultracontractivity of non-symmetric diffusion semigroups in
bounded domains |
| 报
告 人： |
宋仁明
教授 （University of Illinois at Urbana-Champaign） |
| 时间地点： |
2006年5月18日（星期四）下午3:00-4:00 晨兴数学中心110
|
| 摘 要： |
The
notion of intrinsic ultracontractivity, introduced by Davies
and Simon for symmetric semigroups, is a very important concept
and has been studied extensively. However, it seems that, up
to now, no one has introduced the concept of intrinsic ultracontractivity
for non-symmetric semigroups. In this talk, we first introduce
the notion of intrinsic ultracontractivity for non-symmetric
semigroups. We will show that the Dirichlet semigroups of non-symmetric
diffusion semigroups are intrinsic ultracontractive on very
rough domains. |
|
2006年3月
|
| 报告题目： |
Gibbs测度的谱隙估计 |
| 报
告 人： |
吴黎明
教授（法国Blaise Pascal大学， 中科院数学与系统科学研究院（国家杰出青年B类获得者）） |
| 时间地点： |
2006年3月30日（星期四）下午3:00-4:00 |
| 摘 要： |
利用Bocher公式的思想，将Ligget M-ε定理推广到连续spin空间情形，由此得到Gibbs场谱隙的sharp估计。作为应用，讨论SN-模型和离散P(φ)d模型 |
|
2005年12月
|
| 报告题目： |
Zeros
of Random Polynomials |
| 报
告 人： |
方诗赞
教授（法国Bourgogne大学） |
| 时间地点： |
2005年12月19日(星期一)下午3:00-4:40 晨兴110 |
| 摘 要： |
We
shall give a survey on our works, some of them being done jointly
with Tusheng Zhang and Peter Imkeller, about stochastic differential
equations beyond non Lipschitz conditions.. |
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| 报告题目： |
Zeros
of Random Polynomials |
| 报
告 人： |
李文博
教授（美国Univ. of Delaware ） |
| 时间地点： |
2005年12月12日(星期一)下午4:00-5:00 712 |
| 摘 要： |
There
is a long history on the study of the number of real zeros of
a random polynomial whose coefficients are independent, identically
distributed random variables. We first give an overview and
then present new representations and bounds for the decay (positivity)
exponent of the probability that a random polynomial of large
even degree has no real zero. Similar results for multi-variable
random polynomial are also given. Connections with Gaussian
processes and various related probability estimates are discussed..
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2005年9月
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| 报告题目： |
The
Hypergroup Property and Representation of MarkovKernels |
| 报
告 人： |
Professor
Dominique Bakry（University Paul Sabatier, France） |
| 时间地点： |
2005年9月12日（星期一）4:00-5:00 703 |
| 摘 要： |
..
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| 报告题目： |
Rough
Path Theory |
| 报
告 人： |
Professor
Terry Lyons（Fellow of Royal Society Mathematical Institute,
University of Oxford） |
| 时间地点： |
2005年9月5日（星期一）4:00-5:00 712 |
| 摘 要： |
The
theory of rough paths as developed by the Author (and several
others such as Hambly, Ledoux, Coutin, Qian, Friz, ...) aims
to extend the calculus of differential equations to contexts
that are far from differentiable. The methodology has had a
significant impact on classical questions from probability,
but also has connection with topology and geometry. The methodology
extends classical and Ito calculus to many new types of stochastic
forcing outside the classical semi-martingale setting directly.
The key to this theory is to answer the question - when do two
controls produce similar responses. This is also a core question
for the problem for multi-scale analysis where one needs to
summarise small scale behaviour in a way that large scale responses
can be predicted from the summarised information. The question
can be translated into one asking that one characterises the
continuity properties of the Ito map. This is indeed possible
and the Universal Limit theorem proves the (uniform) continuity
of the map taking the forcing control to response for a wide
class of metrics on smooth paths - and the completions of the
space under these metrics give the so called rough paths - giving
insight into the control problem. There are many immediate consequences
of this universal limit theorem within probability theory.
The approach is quite structured, and allows one to give a top
down analysis of a control in terms of a sequence of algebraic
coefficients we call the signature of the control (which have
similarity to a child's precis of a complicated text by a simpler
one and are a non-commutative analogue of Fourier coefficients)
with refinements giving more accurate information about the
control. Hambly and Lyons recently proved that this "signature"
of a control completely characterises a finite length control
up to the appropriate null sets.. |
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2005年6月
|
| 报告题目： |
Existence
of non-trivial harmonic functions on Cartan-Hadamard manifolds
of unbounded curvature |
| 报
告 人： |
Prof.
Anton Thalmaie（University of Poitiers, France ） |
| 时间地点： |
2005.6.3 2:30-3:30pm(数学院思源楼703) |
| 摘 要： |
The
Liouville property of a complete Riemannian manifold M (i.e.,
the question whether there exist non-trivial bounded harmonic
functions on M) has attracted a lot of attention. In particular,
for Cartan-Hadamard manifolds the necessity of lower curvature
bounds is still an open problem. We discuss examples of such
manifolds of unbounded curvature where the limiting angle of
Brownian motion degenerates to a single point on the sphere
at infinity, but where nevertheless the space of bounded harmonic
functions is as rich as in the non-degenerate case.. |
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2005年4月
|
| 报告题目： |
Weak
and Strong Sobolev Spaces over path spaces |
| 报
告 人： |
Dr.
Xue-Mei Li （Nottingham Trent University） |
| 时间地点： |
2005.4.4 4:00-5:00pm(数学院思源楼712) |
| 摘 要： |
The
spaces of paths provide a particularly interesting family of
infinite dimensional spaces for their connection with physics
and stochastic analysis. One of the most imoportant tools in
analysis in Sobolev calculus. Here we investgiate the property
of the basic differential operator d. Although there had been
a surgy of results in this direction, including the establishement
of integration by parts formulae and Sobolev inequalities, the
uniqueness of d had not been investigated. For example on the
Wiener space, spaces of continuous paths on Euclidean spaces,
the closure of d has a characterisation. We ask whether the
same works on path spaces and give a uniqueness result. This
is joint work with K. D. Elworthy.. |
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2005年3月
|
| 报告题目： |
Ergodic
properties of the 2D Navier-Stokes equations I |
| 报
告 人： |
Dr.
Martin Hairer （Warwick University） |
| 时间地点： |
2005.3.21 4:00-5:00pm(晨兴数学中心110 ) |
| 摘 要： |
In
this talk, I will present some recent developments in the study
of the 2D stochastic Navier-Stokes equations driven by translation-invariant
Gaussian noise. I will give a geometric characterisation of
a class of noises that leads to ergodicity and present the main
ideas of the proof of this statement. This talk is based on
a joint work with J. Mattingly.. |
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|
| 报告题目： |
本质谱半径的变分公式在Navier—Stoke方程中的应用 |
| 报
告 人： |
吴黎明教授（武汉大学、法国Blaise Pascal 大学） |
| 时间地点： |
2005.3.11 4:00-5:00pm |
| 摘 要： |
对二维Navier—Stokes方程的离散扰动构成的马氏过程，我们利用本质谱半径的变分公式得到它的非质谱半径估计：
⑴在扰动是高斯且非退化情形下，证明了它在加权空间bvB上的本质半径为0，从而得到大偏差原理。
⑵在扰动是有界的情形下，证明了它在Lipschitz函数空间CLip上有谱隙。
这些结果是二维Navier—Stokes方程随机扰动已知结果的推广和精细。
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2005年1月
|
| 报告题目： |
INTEGRAL
STOCHASTICEQUATION AND ITS ASYMPTOTIC BEHAVIOUR |
| 报
告 人： |
Professor
Hisao Fujita Yashima（Department of MathematicsUniversity of
Turin, ITALY） |
| 时间地点： |
2005.1.10 3:00-4:00pm |
| 摘 要： |
We
consider first a linear integral stochastic equation (Volterra-Ito
equa-tion) with values in Rn. Under a suitable ( and reasonably
general ) condition we prove the uniform boundedness of E(|X(t)|2).
Under the same condition we prove also, for this equation, the
existence of the (unique) invariant measure in a suitably constructed
Hilbert space. This Hilbert spacecontains the "present"
and the "past"of the process. The most part of this
result can be generalized to a class ofnon-linear integral stocastic
equations.. |
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2004年12月
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| 报告题目： |
Stein's
method and discreteprobability approximations |
| 报
告 人： |
夏爱华
教授（Department of Mathematics and Statistics Univ. of Melbourne,
VIC 3010, Australia） |
| 时间地点： |
2004.12.20 5:00-6:00pm |
| 摘 要： |
We
want to approximate for , where is a sum of independent (or
weakly independent) integer-valued random variables with finite
second moments. This talk covers the following two cases.
Case 1: Majority of are small, for example, W counts the number
of occurrences of certain rare events
Case 2: Majority of are relatively large, then the distribution
of should behave like a "discrete normal".
The first case are approximated by Poisson or a modified Poisson
such as compound Poisson, Poisson signed measures with errors
of approximation estimated by Stein-Chen method. Barbour's probabilistic
interpretation of Stein-Chen method for estimating the error
of Poisson approximations not only paved a way for investigating
Poisson process, but also provide an opportunity for studying
other approximations. Xia (1999) give a pure probabilistic proof
of stein bound for Poisson approximation, and the case of approximations
by general distributions on the non-negative integers by Brown
and Xia (2001). The method of Brown and Xia apply to a very
large class of approximation distributions on the non-negative
integers, including Poisson, binomial, negative binomial as
well as a natural class for high-order approximations by probability
distributions rather than signed measures. This offers a comprehensive
solution of case 1.
In terms of case 2, Goldstein and xia (2004) introduce a new
family of discrete distributions and provided a discrete version
of Berry-Esseen theorem showing how members of family approximate
the distribution of in total variation .. |
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2004年11月
|
| 报告题目： |
Potential
theory of specialsubordinators and subordinate killed Brownian
motions |
| 报
告 人： |
宋仁明
教授（Dept. of Math., Univ. of Illinois at Urbana-Champaign） |
| 时间地点： |
2004.11.22 5:00-6:00pm |
| 摘 要： |
In
this talk we will first introduce a class of subordinators called
special subordinators. The class of subordinators is very large
and it includes all the subordinators whose Laplace exponents
are complete Bernstein functions, so it includes all the stable
subordinators. We then present the potential theory of special
subordinators. We then present results on
the potential theory of processes obtained by subordinating
a killed Brownian motion in a bounded Lipschitz domain D by
special subordinators. We will show that there is a one-to-one
correspondence between the nonnegative harmonic functions of
the killed Brownian motion and of the subordinate killed Brownian
motion. By using this correspondence, we will show that both
the Martin boundary and minimal Martin boundary of the subordiante
killed Brownian motion coincide with the Euclidean boundary
of D. We will also establish a boundary Harnack principle for
the positive harmonic functions of subordinate killed Brownian
motions.. |
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| 报告题目： |
Stochastic
Models of Economic Optimization |
| 报
告 人： |
陈木法
院士（北京师范大学数学科学学院） |
| 时间地点： |
2004.11.08 5:00-6:00pm |
| 摘 要： |
Some
stochastic models of economic optimization are discussed in
this paper. Due to the value in practice, the models are quite
attractive. But our knowledge on them is still very limited,
some fundamental problems remain open.
We begin with a short review of the study on some global economic
models (or economy in large scale), the well-known input-output
method and L.K. Hua's fundamental theorem for the stability
of economy. Then, we show that it is necessary to study the
stochastic models. A collapse theorem for a non-controlling
stochastic economic system is introduced. In the analysis of
the system, the products of random matrices play a critical
role. Especially, the first eigenvalue, the corresponding eigenfunctions
and an ergodic theorem of Markov chains play a nice role here.
Partial proofs are included. Some challenge open problems are
also mentioned.. |
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2004年10月
|
| 报告题目： |
Random
Graphs andStochastic Complex Networks |
| 报
告 人： |
马志明 院士（中科院数学院应用数学所） |
| 时间地点： |
2004.10.25 5:00-6:00pm |
| 摘 要： |
The
last few years have witnessed a tremendous activity devoted
to the characterization and understanding of growing networks
and graphs in various systems such as the Internet, social networks,
and biological networks. In this talk we shall first briefly
review some results on the classical random graphs. And then
we review some recent discussion on the study of stochastic
complex networks arising from the real world. Among many hundreds
of interesting papers we shall introduce in particular:
(i) "ten leading questions for network research" suggested
by physicists in this area including A.L. Barabasi, J.F.F. Mendes
el al;
(ii) view points of some mathemati- cians including D. Aldous,
B. Bollobos and R. Durrett.. |
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|
| 报告题目： |
An
Invitation to Random Matrices |
| 报
告 人： |
骆顺龙
研究员（中科院数学院应用数学所） |
| 时间地点： |
2004.10.11 5:00-6:00pm |
| 摘 要： |
Random
matrices have their origin in multivariate statisticalanalysis
(Pao-lu Hsu (许宝禄）, Wishart, 1930s). They were in-troduced into
physics by Wigner in the 1950s to model complex systems in nuclear
physics. The basic idea underlying this approach is the assumption
that the local statistical behavior of the energy levels of
suciently complicated systems can be stim-ulated by that of
the eigenvalues of random atrices. Also in the 1950s, Loo-keng
Hua(华罗庚) calculated the volumes of various classical domains
and the othogonal (unitary) groups which are important matrix
spaces and thus paved the way for introducing natural probability
distributions on such spaces. In the 1970s,Montgomery and Dyson
discovered that the pair correlations of the zeros of the Riemann
zeta function seems behave like that of the eigenvalues of certain
random matrices. Around 1990s, Voiculescu discovered that asymptotically
random matrices can serve as a natural model for the newly emerging
held of free prob-ability. Now random matrices have developed
into a profound enterprise which has fascinating and mysterious
relations with,and deep applications in, statistics and probability,
physics, number theory, operator algebras, and many others.
This talk will provide a brief account of some stories around
random matrices from a historical perspective. |
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2004年9月
|
| 报告题目： |
Vicious
Walks, Schur Functions and Random Matrix Theory |
| 报
告 人： |
Professor
Makoto KATORI (Chuo University, Tokyo, Japan） |
| 时间地点： |
2004.9.27 5:00-6:00pm |
| 摘 要： |
The
system of one-dimensional symmetric simple random walks,in which
none of walkers have met others in a given time period,is called
the vicious walker model. It was introduced by Michael Fisher
and applications of the model to various wetting and melting
phenomena were described in his Boltzmann medal lecture in 1984.In
the present talk, I will try to explain interesting connections
among representation theory, random matrix theory and probability
theory, using this simple diffusion particle system: Each vicious
walk of N walkers is represented by an N-tuple of nonintersecting
lattice paths on the spatio-temporal plane. We show that there
is established a simple bijection between nonintersecting lattice
paths and semistandard Young tableaux. Based on this bijection
and some knowledge of symmetric polynomials called the Schur
functions, we can give a determinantal expression to the partition
function of vicious walks, which is regarded as a special case
of Karlin-McGregor formula in probability theory. Due to a property
of Schur function, we can take the diffusion scaling limit of
the vicious walks and define a noncolliding system of Brownian
particles. This diffusion process solves the stochastic differential
equations with the drift terms acting as the repulsive two-body
forces proportional to the inverse of distances between particles,
and thus it is idetified with Dyson's Brownian motion model.
In other words, the obtained noncolliding system of Brownian
particles is equivalent in distribution with the eigenvalue
process of a Hermitian matrix-valued process.. |
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|
| 报告题目： |
Recent
development on interacting diffusion systems |
| 报
告 人： |
Professor
Tokuzo Shiga (Tokyo Institute ofTechnology） |
| 时间地点： |
2004.9.13 5:00-6:00pm |
| 摘 要： |
..
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|
| 报告题目： |
A
Relativistic Diffusion |
| 报
告 人： |
Prof.
Yves Le Jan ((University Paris - Sud, Orsay, RANCE 巴黎11大概率统计实验室主任)
|
| 时间地点： |
2004.9.13 4:00-5:00pm |
| 摘 要： |
The
relativistic motion of a point mass with Brownian 4-velocity
is defined in the general relativistic framework, extending
a previous work of Dudley done in the context of special relativity.
The exemple of the Schwartzschild space is studied in some detail
especially to determine the asymptotic behaviour of the motion..
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