SOBOLEV DIFFERENTIABLE FLOWS OF SDES WITH LOCAL SOBOLEV AND SUPER-LINEAR GROWTH COEFFICIENTS

• 成果类型: Article
• 署名作者: Xie, Longjie; Zhang, Xicheng
• 署名单位: Wuhan University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1057
• 发表日期: 2016
• 页码: 3661-3687
• 关键词: stochastic-evolution equations; diffusion-coefficients; transport-equation; strong uniqueness; measurable drift; SPACES

摘要

By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility to the associated diffusion semigroup.