Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/238129
Year of Publication: 
2021
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 651
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
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.
Subjects: 
Stochastic filtering
singularly controlled systems
reference probability measure
Zakai equation
Kushner-Stratonovich equation
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Working Paper

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