On parabolic inequalities for generators of diffusions with jumps

• 成果类型: Article
• 署名作者: Bogachev, Vladimir I.; Roeckner, Michael; Shaposhnikov, Stanislav V.
• 署名单位: Lomonosov Moscow State University; St Tikhons's University; University of Bielefeld
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0485-0
• 发表日期: 2014
• 页码: 465-476
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; Absolute continuity; smooth densities

摘要

We prove absolute continuity of space-time probabilities satisfying certain parabolic inequalities for generators of diffusions with jumps. As an application, we prove absolute continuity of transition probabilities of singular diffusions with jumps under minimal conditions that ensure absolute continuity of the corresponding diffusions without jumps.