Smoothing properties of McKean-Vlasov SDEs

• 成果类型: Article
• 署名作者: Crisan, Dan; McMurray, Eamon
• 署名单位: Imperial College London
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0774-0
• 发表日期: 2018
• 页码: 97-148
• 关键词: mean-field games; differential-equations; particle method; systems

摘要

In this article, we develop integration by parts formulae on Wiener space for solutions of SDEs with general McKean-Vlasov interaction and uniformly elliptic coefficients. These integration by parts formulae hold both for derivatives with respect to a real variable and derivatives with respect to a measure understood in the sense of Lions. They allows us to prove the existence of a classical solution to a related PDE with irregular terminal condition. We also develop bounds for the derivatives of the density of the solutions of McKean-Vlasov SDEs.