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Numerical method
for expectations of piecewise deterministic Markov
processes
Adrien Brandejsky, Benoîte de Saporta and François Dufour |
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Vol. 7 (2012), No. 1, 63–104
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Abstract |
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We present a numerical method to compute expectations of functionals of a piecewise deterministic Markov process. We discuss time dependent functionals as well as deterministic time horizon problems. Our approach is based on the quantization of an underlying discrete-time Markov chain. We obtain bounds for the rate of convergence of the algorithm. The approximation we propose is easily computable and is flexible with respect to some of the parameters defining the problem. An example illustrates the paper. |
Keywords
expectation, piecewise deterministic Markov processes,
quantization, numerical method
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Mathematical Subject Classification 2010
Primary: 60J25, 65C20
Secondary: 60K10
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Milestones
Received: 6 May 2011
Revised: 8 November 2011
Accepted: 5 December 2011
Published: 28 March 2012
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Authors |
| Adrien Brandejsky | ||
| INRIA Bordeaux Sud-Ouest, team
CQFD F-33400 Talence France |
Université de Bordeaux, IMB, UMR
5251 F-33400 Talence France |
CNRS, IMB, UMR 5251 F-33400 Talence France |
| Benoîte de Saporta | ||
| Université de Bordeaux, Gretha, UMR
5113 F-33400 Talence France |
CNRS, Gretha, UMR 5113, IMB, UMR
5251 F-33400 Talence France |
INRIA Bordeaux Sud-Ouest, team
CQFD F-33400 Talence France |
| François Dufour | ||
| Université de Bordeaux, IMB, UMR
5251 F-33400 Talence France |
CNRS, IMB, UMR 5251 F-33400 Talence France |
INRIA Bordeaux Sud-Ouest, team
CQFD F-33400 Talence France |
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