Kolmogorov equations on spaces of measures associated to nonlinear filtering processes

Mattia Martini

Stochastic Processes and their Applications, 2023, vol. 161, issue C, 385-423

Abstract: We introduce and study some backward Kolmogorov equations associated to filtering problems. In the stochastic filtering framework, SDEs for measure-valued processes arise naturally (Zakai and Kushner–Stratonovich equation). The associated Kolmogorov equations have been intensively studies, assuming that the measure-valued processes admit a density and then by exploiting stochastic calculus in Hilbert spaces.

Keywords: Backward Kolmogorov equations; Stochastic filtering; Measure-valued processes; Differential equations on spaces of measures (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:161:y:2023:i:c:p:385-423

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DOI: 10.1016/j.spa.2023.04.013

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