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Controlled Filtered Poisson Processes

Author

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  • Mario Lefebvre

    (Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succursale Centre-Ville, Montréal, QC H3C 3A7, Canada)

Abstract

Filtered Poisson processes are used as models in various applications, in particular in statistical hydrology. In this paper, controlled filtered Poisson processes are considered. The aim is to minimize the expected time that the process will spend in the continuation region. The dynamic programming equation satisfied by the value function is derived. To obtain the value function, and hence the optimal control, a non-linear integro-differential equation must be solved, subject to the appropriate boundary conditions. Various cases for the size of the jumps are treated and explicit results are obtained.

Suggested Citation

  • Mario Lefebvre, 2025. "Controlled Filtered Poisson Processes," Mathematics, MDPI, vol. 13(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:284-:d:1569038
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    References listed on IDEAS

    as
    1. Fares Alazemi & Khalifa Es-Sebaiy & Youssef Ouknine, 2019. "Efficient and superefficient estimators of filtered Poisson process intensities," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(7), pages 1682-1692, April.
    2. Grant, James A. & Szechtman, Roberto, 2021. "Filtered poisson process bandit on a continuum," European Journal of Operational Research, Elsevier, vol. 295(2), pages 575-586.
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