Hypoellipticity for filtering problems of partially observable diffusion processes

• 成果类型: Article
• 署名作者: Krylov, N. V.
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0557-9
• 发表日期: 2015
• 页码: 687-718
• 关键词: equations

摘要

We prove that under Hormander's type conditions on the coefficients of the unobservable component of a partially observable diffusion process the filtering density is infinitely differentiable and can be represented as the integral of an infinitely differentiable kernel against the prior initial distribution. These results are derived from more general results obtained for SPDEs. One of the main novelties of the paper is the existence and smoothness of the kernel, another one is that we allow the coefficients of our partially observable process to be just measurable with respect to the time variable and Lipschitz continuous with respect to the observation variable.