Estimates for invariant probability measures of degenerate SPDEs with singular and path-dependent drifts

• 成果类型: Article
• 署名作者: Wang, Feng-Yu
• 署名单位: Tianjin University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0827-4
• 发表日期: 2018
• 页码: 1181-1214
• 关键词: functional inequalities; harnack inequality; strong uniqueness; sdes; EQUATIONS; gradient; THEOREM; SPACES; heat

摘要

In terms of a nice reference probability measure, integrability conditions on the path-dependent drift are presented for (infinite-dimensional) degenerate PDEs to have regular positive solutions. To this end, the corresponding stochastic (partial) differential equations are proved to possess the weak existence and uniqueness of solutions, as well as the existence, uniqueness and entropy estimates of invariant probability measures. When the reference measure satisfies the log-Sobolev inequality, Sobolev estimates are derived for the density of invariant probability measures. Some results are new even for non-degenerate SDEs with path-independent drifts. The main results are applied to nonlinear functional SPDEs and degenerate functional SDEs/SPDEs.