CAUCHY PROBLEM OF STOCHASTIC KINETIC EQUATIONS

• 成果类型: Article
• 署名作者: Zhang, Xiaolong; Zhang, Xicheng
• 署名单位: Beijing Institute of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1961
• 发表日期: 2024
• 页码: 148-202
• 关键词: hypoelliptic regularity; schauder; EXISTENCE; SPACES; noise

摘要

In this paper we establish the optimal regularity estimates for the Cauchy problem of stochastic kinetic equations with random coefficients in anisotropic Besov spaces. As applications, we study the nonlinear filtering problem for a degenerate diffusion process, and obtain the existence and regularity of conditional probability densities under a few assumptions. Moreover, we also show the well-posedness for a class of super-linear growth stochastic kinetic equations driven by velocity-time white noises.