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- Title
Hypoellipticity for filtering problems of partially observable diffusion processes.
- Authors
Krylov, N.
- Abstract
We prove that under Hörmander'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.
- Subjects
HYPOELLIPTIC operators; DIFFUSION processes; LIPSCHITZ spaces; SMOOTHNESS of functions; KERNEL (Mathematics); EXISTENCE theorems
- Publication
Probability Theory & Related Fields, 2015, Vol 161, Issue 3/4, p687
- ISSN
0178-8051
- Publication type
Article
- DOI
10.1007/s00440-014-0557-9