Non-failable approximation method for conditioned distributions

TL;DR

This paper introduces a new, always well-defined particle system method for approximating conditioned distributions of stochastic processes, ensuring convergence and applicability to quasi-stationary distributions, demonstrated through neutron transport models.

Contribution

The paper presents a novel particle system approach that overcomes failability issues, with proven uniform convergence and applicability to quasi-stationary distributions.

Findings

The new particle system is always well-defined.

The method converges uniformly in time.

Application to neutron transport models demonstrates effectiveness.

Abstract

We consider a general method for the approximation of the distribution of a process conditioned to not hit a given set. Existing methods are based on particle system that are failable, in the sense that, in many situations , they are not well defined after a given random time. We present a method based on a new particle system which is always well define. Moreover , we provide sufficient conditions ensuring that the particle method converges uniformly in time. We also show that this method provides an approximation method for the quasi-stationary distribution of Markov processes. Our results are illustrated by their application to a neutron transport model.