Numerical method for expectations of piecewise-determistic Markov processes

TL;DR

This paper introduces a flexible, easily computable numerical method based on quantization for estimating expectations of functionals in piecewise-deterministic Markov processes, applicable to time-dependent and horizon problems.

Contribution

The paper develops a novel quantization-based numerical approach for expectations in piecewise-deterministic Markov processes, including convergence bounds and practical examples.

Findings

The method provides accurate expectations with proven convergence rates.

It is adaptable to various parameters and problem types.

Two illustrative examples demonstrate its effectiveness.

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. Two examples illustrate the paper.