Singular HJB equations with applications to KPZ on the real line

• 成果类型: Article
• 署名作者: Zhang, Xicheng; Zhu, Rongchan; Zhu, Xiangchan
• 署名单位: Wuhan University; Beijing Institute of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01137-w
• 发表日期: 2022
• 页码: 789-869
• 关键词: stochastic heat-equations; paracontrolled distributions; weak universality; burgers; CONSTRUCTION; noise; MODEL

摘要

This paper is devoted to studying Hamilton-Jacobi-Bellman equations with distribution-valued 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 Holder 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 Holder spaces for KPZ type equations on the real line, as well as modified KPZ equations for which the Cole-Hopf transformation is not applicable.