contribution à l'étude des processus Markoviens déterministes par morceaux. Etude d'un cas-test de la sûreté de fonctionnement et Problème d'arrêt optimal à horizon aléatoire

Karen Gonzalez 1, 2
1 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Piecewise Deterministic Markov Processes (PDMP's) have been introduced in the literature by M.H.A. Davis as a general class of stochastics models. PDMP's are a family of Markov processes involving deterministic motion punctuated by random jumps. In a rst part, PDMP's are used to compute probabilities of top events for a case-study of dynamic reliability (the heated tank system) with two di erent methods : the rst one is based on the resolution of the di erential system giving the physical evolution of the tank and the second uses the computation of the functional of a PDMP by a system of integro-di erential equations. In the second part, we propose a numerical method to approximate the value function for the optimal stopping problem of a PDMP. Our approach is based on quantization of the postjump location and inter-arrival time of the Markov chain naturally embedded in the PDMP, and path-adapted time discretization grids. It allows us to derive bounds for the convergence rate of the algorithm and to provide a computable epsilon-optimal stopping time.
Document type :
Theses
Liste complète des métadonnées

Cited literature [85 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00938591
Contributor : Benoîte de Saporta <>
Submitted on : Wednesday, January 29, 2014 - 2:43:11 PM
Last modification on : Thursday, January 11, 2018 - 6:22:11 AM
Document(s) archivé(s) le : Sunday, April 9, 2017 - 2:28:18 AM

Identifiers

  • HAL Id : tel-00938591, version 1

Collections

Citation

Karen Gonzalez. contribution à l'étude des processus Markoviens déterministes par morceaux. Etude d'un cas-test de la sûreté de fonctionnement et Problème d'arrêt optimal à horizon aléatoire. Probabilités [math.PR]. Université Sciences et Technologies - Bordeaux I, 2010. Français. ⟨tel-00938591⟩

Share

Metrics

Record views

313

Files downloads

175