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

Calvia A, Ferrari G (2021) Center for Mathematical Economics Working Papers; 651.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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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 $\nu$ 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.

AMS 2020: 93E11, 60H15; 60J25, 60J76
Stichworte
Stochastic filtering; singularly controlled systems; reference probability measure; Zakai equation; Kushner-Stratonovich equation
Erscheinungsjahr
2021
Serientitel
Center for Mathematical Economics Working Papers
Band
651
Seite(n)
26
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2955492

Zitieren

Calvia A, Ferrari G. Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control. Center for Mathematical Economics Working Papers. Vol 651. Bielefeld: Center for Mathematical Economics; 2021.
Calvia, A., & Ferrari, G. (2021). Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control (Center for Mathematical Economics Working Papers, 651). Bielefeld: Center for Mathematical Economics.
Calvia, A., and Ferrari, G. (2021). Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control. Center for Mathematical Economics Working Papers, 651, Bielefeld: Center for Mathematical Economics.
Calvia, A., & Ferrari, G., 2021. Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control, Center for Mathematical Economics Working Papers, no.651, Bielefeld: Center for Mathematical Economics.
A. Calvia and G. Ferrari, Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control, Center for Mathematical Economics Working Papers, vol. 651, Bielefeld: Center for Mathematical Economics, 2021.
Calvia, A., Ferrari, G.: Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control. Center for Mathematical Economics Working Papers, 651. Center for Mathematical Economics, Bielefeld (2021).
Calvia, Alessandro, and Ferrari, Giorgio. Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control. Bielefeld: Center for Mathematical Economics, 2021. Center for Mathematical Economics Working Papers. 651.
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2021-06-10T13:49:47Z
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