Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control

Abstract This paper deals with a nonlinear filtering problem in which multi-dimensional signal process is additively affected by $$\nu $$ ν whose components have paths of bounded variation. The presence the prevents from directly applying classical results and novel estimates need to be derived. By making use so-called reference probability measure approach, we derive Zakai equation satisfied unnormalized process, then deduce corresponding Kushner–Stratonovich equation. Under condition that jump times do not accumulate over considered time horizon, show unique solution equation, class measure-valued processes having square-integrable density. Our analysis paves way study stochastic control problems where decision maker can exert singular controls order adjust dynamics an unobservable Itô-process.