Filtering equations for partially observable diffusion processes with Lipschitz continuous coefficients

Abstract

We present several results on smoothness in $L_p$ sense of filtering densities under the Lipschitz continuity assumption on the coefficients of a partially observable diffusion processes. We obtain them by rewriting in divergence form filtering equation which are usually considered in terms of formally adjoint to operators in nondivergence form.

25 pages

Cited by in corpus (1)

• SPDEs in divergence form with VMO coefficients and filtering theory of partially observable diffusion processes with Lipschitz coefficients