Singular HJB equations with applications to KPZ on the real line

时间:2020.12.27 15:40-16:40

地点:腾讯会议 177 249 810





In this talk I will report a joint work with Rongchan Zhu and Xiangchan Zhu about singular HJB equations. In this work we study the Hamilton-Jacobi-Bellman equations with distribution-valued coefficients, which is not well-defined in the classical sense and shall be understood by using paracontrolled distribution method introduced by Gubinelli-Imkeller-Perkowskii. By a new characterization of weighted H\older space and Zvonkin's transformation we prove some new a priori estimates, and therefore, establish the global well-posedness for singular HJB equations. As an application, the global well-posedness for KPZ equations on the real line in polynomial weighted H\older spaces is obtained without using Cole-Hopf's transformation.