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Kolmogorov equations on spaces of measures associated to nonlinear filtering processes

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  • Martini, Mattia

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.

Suggested Citation

  • Martini, Mattia, 2023. "Kolmogorov equations on spaces of measures associated to nonlinear filtering processes," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 385-423.
    • Handle: RePEc:eee:spapps:v:161:y:2023:i:c:p:385-423
    DOI: 10.1016/j.spa.2023.04.013
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    References listed on IDEAS

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    1. Bandini, Elena & Cosso, Andrea & Fuhrman, Marco & Pham, Huyên, 2019. "Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 674-711.
    2. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704.
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