Interacting Particle System-based Estimation of Reach Probability for a Generalized Stochastic Hybrid System

This paper studies estimation of reach probability for a generalized stochastic hybrid system (GSHS). For diffusion processes a well-developed approach in reach probability estimation is to introduce a suitable factorization of the reach probability and then to estimate these factors through simulation of an Interacting Particle System (IPS). The theory of this IPS approach has been extended to arbitrary strong Markov processes, which includes GSHS executions. Because Monte Carlo simulation of GSHS particles involves sampling of Brownian motion as well as sampling of random discontinuities, the practical elaboration of the IPS approach for GSHS is not straightforward. The aim of this paper is to elaborate the IPS approach for GSHS by using complementary Monte Carlo sampling techniques. For a simple GSHS example, it is shown that and why the specific technique selected for sampling discontinuities can have a major influence on the effectiveness of IPS in reach probability estimation.