Numerical methods for the exit time of a piecewise-deterministic Markov process

Details Numerical methods for the exit time of a piecewise-deterministic Markov process Numerical methods for the exit time of a piecewise-deterministic Markov process

2010-12-13

arxiv.org/abs/1012.2659v2

Mathematics

Probability

Scientific paper

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. An academic example and a model from the reliability field illustrate the paper.

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