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Preprints, Working Papers, ... Year : 2023

Minimum Contrast Estimators for Piecewise Deterministic Markov Processes

Abstract

The main goal of this paper is to study the minimum contrast estimator (MCE) approach for the parameter estimation problem of piecewise deterministic Markov processes (PDMPs), associated to adaptive control problems. It is assumed that the control acts continuously on the jump intensity λ and on the transition measure Q of the process, as well as on the costs, and that these parameters depend on an unknown parameter $\beta^\ast$. One of our objective is to introduce a minimum contrast estimator (βn)n∈N for the family of PDMPs. Sufficient conditions are then presented to ensure that $(\beta_n)$ is a strongly consistent estimator of $\beta^\ast$. It should be noticed that PDMPs are characterized by a deterministic motion punctuated by random jumps (either spontaneous or due to the flow touching a boundary), which brings new challenges in the analysis of the problem. The paper is concluded with a numerical example for the adaptive discounted control of PDMPs.
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Dates and versions

hal-04337828 , version 1 (12-12-2023)

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  • HAL Id : hal-04337828 , version 1

Cite

Alexandre Genadot, François Dufour, Oswaldo Luiz Do Valle Costa. Minimum Contrast Estimators for Piecewise Deterministic Markov Processes. 2023. ⟨hal-04337828⟩
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