Vol. 7, No. 1, 2012

Download this article
Download this article For screen
For printing
Recent Issues
Volume 12, Issue 1
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 1
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 1
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 1
Volume 3, Issue 1
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
Subscriptions
Editorial Board
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Numerical method for expectations of piecewise deterministic Markov processes

Adrien Brandejsky, Benoîte de Saporta and François Dufour

Vol. 7 (2012), No. 1, 63–104
Abstract

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
Mathematical Subject Classification 2010
Primary: 60J25, 65C20
Secondary: 60K10
Milestones
Received: 6 May 2011
Revised: 8 November 2011
Accepted: 5 December 2011
Published: 28 March 2012
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