Numerical method for expectations of piecewise deterministic Markov processes
Adrien Brandejsky, Benoîte de Saporta, François Dufour · Communications in Applied Mathematics and Computational Science · 2012
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.1. Introduction 63 2. Definitions and assumptions 67 3. Expectation 71 4. Approximation scheme 74 5. Time-dependent functionals 78 6. Numerical results 89 7. Conclusion 97 Appendix A. Lipschitz continuity of F , G and v n 97 Appendix B. Relaxed assumption on the running cost function 101 Appendix C. Proof of Theorem 4.5 103