Model problem for integro-differential Zakai equation with discontinuous observation processes in H\"older spaces

TL;DR

This paper investigates the existence and uniqueness of solutions to a stochastic parabolic integro-differential equation related to nonlinear filtering with jump processes, focusing on solutions in Hölder spaces.

Contribution

It provides new results on the well-posedness of Zakai equations with discontinuous observations in Hölder spaces, addressing a complex filtering problem.

Findings

Proved existence of solutions in Hölder spaces.

Established uniqueness under certain conditions.

Applied to nonlinear filtering with jump signals and observations.

Abstract

The existence and uniqueness of solutions of the Cauchy problem to a a stochastic parabolic integro-differential equation is investigated. The equattion considered arises in nonlinear filtering problem with a jump signal process and jump observation.