Speaker: 王诚石，复旦大学           

Title: Skew Brownian flow: a new approach

Language: Chinese 

Time & Venue: 2024.05.31 14:45-15:25  南楼N620

Abstract: The skew Brownian motion is constructed by assigning signs to Brownian excursions away from 0, each excursion being positive with probability p and negative with probability 1-p. It can equivalently (Harrison-Shepp, 1981) be seen as the strong solution of the SDE dX_t=dB_t + (2p-1) dL_t(X) where L_t(X) denotes the local time of the diffusion at 0. The skew Brownian flow as studied by Burdzy-Chen (2001) and Burdzy-Kaspi (2004) is the flow of solutions driven by the same Brownian motion but starting from any time-space point in the plane. In this talk, I will give results on the properties of meeting level processes and the exact Hausdorff dimension of bifurcation times of different types appeared in the skew Brownian flow. To prove them, I will introduce another coalescing stochastic flow, called the BESQ flow, and give a connection between these two flows. Joint work with Elie Aïdékon and Yaolin Yu