Advances in Applied Probability

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

Adrien Brandejsky, Benoîte De Saporta, and François Dufour

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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.

Article information

Source
Adv. in Appl. Probab., Volume 44, Number 1 (2012), 196-225.

Dates
First available in Project Euclid: 8 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.aap/1331216650

Digital Object Identifier
doi:10.1239/aap/1331216650

Mathematical Reviews number (MathSciNet)
MR2951552

Zentralblatt MATH identifier
1244.60073

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces 65C20: Models, numerical methods [See also 68U20]
Secondary: 60K10: Applications (reliability, demand theory, etc.)

Keywords
Exit time piecewise-deterministic Markov process quantization numerical method

Citation

Brandejsky, Adrien; De Saporta, Benoîte; Dufour, François. Numerical methods for the exit time of a piecewise-deterministic Markov process. Adv. in Appl. Probab. 44 (2012), no. 1, 196--225. doi:10.1239/aap/1331216650. https://projecteuclid.org/euclid.aap/1331216650


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