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

Alessandro Calvia and Giorgio Ferrari
Additional contact information
Alessandro Calvia: Center for Mathematical Economics, Bielefeld University
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University

No 651, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: 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.

Keywords: Stochastic filtering; singularly controlled systems; reference probability measure; Zakai equation; Kushner-Stratonovich equation (search for similar items in EconPapers)
Pages: 26
Date: 2021-06-10
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://pub.uni-bielefeld.de/download/2955492/2955493 First Version, 2021 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:651

Access Statistics for this paper

More papers in Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University Contact information at EDIRC.
Bibliographic data for series maintained by Bettina Weingarten ().