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March 2012 Numerical methods for the exit time of a piecewise-deterministic Markov process
Adrien Brandejsky, Benoîte De Saporta, François Dufour
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Adv. in Appl. Probab. 44(1): 196-225 (March 2012). DOI: 10.1239/aap/1331216650

Abstract

We present a numerical method to compute the survival function and the moments of the exit time for a piecewise-deterministic Markov process (PDMP). Our approach is based on the quantization of an underlying discrete-time Markov chain related to the PDMP. The approximation we propose is easily computable and is even flexible with respect to the exit time we consider. We prove the convergence of the algorithm and obtain bounds for the rate of convergence in the case of the moments. We give an academic example and a model from the reliability field to illustrate the results of the paper.

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Adrien Brandejsky. Benoîte De Saporta. François Dufour. "Numerical methods for the exit time of a piecewise-deterministic Markov process." Adv. in Appl. Probab. 44 (1) 196 - 225, March 2012. https://doi.org/10.1239/aap/1331216650

Information

Published: March 2012
First available in Project Euclid: 8 March 2012

zbMATH: 1244.60073
MathSciNet: MR2951552
Digital Object Identifier: 10.1239/aap/1331216650

Subjects:
Primary: 60J25, 65C20
Secondary: 60K10

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 1 • March 2012
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