TY  - GEN
AB  - This paper deals with a nonlinear filtering problem in which a multi-dimensional signal process is additively affected by a process $\nu$ whose components have paths of bounded variation. The presence of the process $\nu$ prevents from directly applying classical results and novel estimates need to be derived. By making use of the so-called reference probability measure approach, we derive the Zakai equation satisfied by the unnormalized filtering process, and then we deduce the corresponding Kushner-Stratonovich equation. Under the condition that the jump times of the process $\nu$ do not accumulate over the considered time horizon, we show that the unnormalized filtering process is the unique solution to the Zakai equation, in the class of measure-valued processes having a square-integrable density. Our analysis paves the way to the study of stochastic control problems where a decision maker can exert singular controls in order to adjust the dynamics of an unobservable Itô-process.
DA  - 2021
KW  - Stochastic filtering
KW  - singularly controlled systems
KW  - reference probability measure
KW  - Zakai equation
KW  - Kushner-Stratonovich equation
LA  - eng
PY  - 2021
SN  - 0931-6558
SP  - 26-
TI  - Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29554928
Y2  - 2024-11-22T08:03:52
ER  -