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

Calvia A, Ferrari G (2022)
Applied Mathematics and Optimization 85(2): 12.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Calvia, Alessandro; Ferrari, GiorgioUniBi
Abstract / Bemerkung
This paper deals with a nonlinear filtering problem in which a multi-dimensional signal process is additively affected by a process v whose components have paths of bounded variation. The presence of the process v prevents from directly applying classical results and novel estimates need to be derived. By making use of the socalled 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 v 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 Ito-process.
Stichworte
Stochastic filtering; Singularly controlled systems; Reference; probability measure; Zakai equation; Kushner-Stratonovich equation
Erscheinungsjahr
2022
Zeitschriftentitel
Applied Mathematics and Optimization
Band
85
Ausgabe
2
Art.-Nr.
12
ISSN
0095-4616
eISSN
1432-0606
Page URI
https://pub.uni-bielefeld.de/record/2962706

Zitieren

Calvia A, Ferrari G. Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control. Applied Mathematics and Optimization . 2022;85(2): 12.
Calvia, A., & Ferrari, G. (2022). Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control. Applied Mathematics and Optimization , 85(2), 12. https://doi.org/10.1007/s00245-022-09822-x
Calvia, A., and Ferrari, G. (2022). Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control. Applied Mathematics and Optimization 85:12.
Calvia, A., & Ferrari, G., 2022. Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control. Applied Mathematics and Optimization , 85(2): 12.
A. Calvia and G. Ferrari, “Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control”, Applied Mathematics and Optimization , vol. 85, 2022, : 12.
Calvia, A., Ferrari, G.: Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control. Applied Mathematics and Optimization . 85, : 12 (2022).
Calvia, Alessandro, and Ferrari, Giorgio. “Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control”. Applied Mathematics and Optimization 85.2 (2022): 12.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar