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

Julien Chiquet and Nikolaos Limnios

Statistics & Probability Letters, 2008, vol. 78, issue 12, 1397-1403

Abstract: 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.

Date: 2008
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