A method to compute the transition function of a piecewise deterministic Markov process with application to reliability

Julien Chiquet (1) , Nikolaos Limnios (1)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

We study the time evolution of an increasing stochastic process governed by a first-order stochastic differential system. This defines a particular piecewise deterministic Markov process (PDMP). We consider a Markov renewal process (MRP) associated to the PDMP and its Markov renewal equation (MRE) which is solved in order to obtain a closed-form solution of the transition function of the PDMP. It is then applied in the framework of survival analysis to evaluate the reliability function of a given system. We give a numerical illustration and we compare this analytical solution with the Monte Carlo estimator.

Mots clés: Piecewise deterministic Markov Process; Markov Renewal Process; Transition function; Reliability; Survival Analysis

Domaines: Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Julien Chiquet, Nikolaos Limnios. A method to compute the transition function of a piecewise deterministic Markov process with application to reliability. Statistics and Probability Letters, 2007, 78 (12), pp.1397-1403. ⟨10.1016/j.spl.2007.12.016⟩. ⟨hal-00260732⟩