Marginalization for rare event simulation in switching diffusions

TL;DR

This paper introduces a novel approach using the Wonham filter combined with splitting techniques to efficiently estimate rare event probabilities in switching diffusions, reducing variance and simplifying sampling.

Contribution

It proposes a new method that leverages the Wonham filter for rare event simulation in switching diffusions, improving efficiency over classical methods.

Findings

Reduced asymptotic variance in probability estimates

Eliminated the need to sample discrete components

Enhanced efficiency of rare event simulation

Abstract

In this paper we use splitting technique to estimate the probability of hitting a rare but critical set by the continuous component of a switching diffusion. Instead of following classical approach we use Wonham filter to achieve multiple goals including reduction of asymptotic variance and exemption from sampling the discrete components.