Nonlinear filtering of partially observed systems arising in singular stochastic optimal control

Arbeitspapier

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 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 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 Itô-process.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: Center for Mathematical Economics Working Papers ; No. 651

Klassifikation und Themen

• Klassifikation: Wirtschaft
• Thema: Stochastic filtering ; singularly controlled systems ; reference probability measure ; Zakai equation ; Kushner-Stratonovich equation

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Calvia, Alessandro ; Ferrari, Giorgio
• Ereignis: Veröffentlichung
• (wer): Bielefeld University, Center for Mathematical Economics (IMW)
• (wo): Bielefeld
• (wann): 2021

Weitere Informationen

• Handle: http://hdl.handle.net/10419/238129
• URN: urn:nbn:de:0070-pub-29554928
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ