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Minimum Contrast Estimators for Piecewise Deterministic Markov Processes

hal.structure.identifierMéthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
dc.contributor.authorGENADOT, Alexandre
hal.structure.identifierMéthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierInstitut Polytechnique de Bordeaux [Bordeaux INP]
dc.contributor.authorDUFOUR, François
hal.structure.identifierUniversidade de São Paulo = University of São Paulo [USP]
dc.contributor.authorCOSTA, Oswaldo Luiz Do Valle
dc.date.accessioned2024-04-04T02:32:03Z
dc.date.available2024-04-04T02:32:03Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190351
dc.description.abstractEnThe 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.
dc.language.isoen
dc.subject.enMinimum contrast estimator
dc.subject.enMarkov decision process MDP
dc.subject.enPiecewise deterministic Markov Process
dc.title.enMinimum Contrast Estimators for Piecewise Deterministic Markov Processes
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
dc.subject.halSciences de l'Homme et Société/Méthodes et statistiques
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-04337828
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04337828v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=GENADOT,%20Alexandre&DUFOUR,%20Fran%C3%A7ois&COSTA,%20Oswaldo%20Luiz%20Do%20Valle&rft.genre=preprint


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