This paper is devoted to studying Hamilton-Jacobi-Bellman equations with distributionvalued coefficients, which are not well-defined in the classical sense and are understood by using the paracontrolled distribution method introduced in (Gubinelli et al. in Forum Math Pi 3(6):1, 2015). By a new characterization of weighted Hölder spaces and Zvonkin’s transformation we prove some new a priori estimates, and therefore establish the global well-posedness for singular HJB equations. As applications, we obtain global well-posedness in polynomial weighted Hölder spaces for KPZ type equations on the real line, as well as modified KPZ equations for which the Cole– Hopf transformation is not applicable.Xicheng Zhang XichengZhang@gmail.com School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
Rongchan Zhu zhurongchan@126.com Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
Xiangchan Zhu zhuxiangchan@126.com Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
地址 北京市海淀区中关村东路55号 思源楼6-7层 南楼5-6、8层 邮编：100190 电子邮箱：iam@amss.ac.cn
