A sequential Monte Carlo approach to computing tail probabilities in stochastic models

TL;DR

This paper presents a sequential Monte Carlo method that efficiently estimates rare event probabilities in multidimensional Markov models using importance sampling and resampling techniques.

Contribution

It introduces a martingale-based approach to optimize resampling weights, achieving logarithmic efficiency in large deviation probability estimation.

Findings

Resampling weights can be chosen to improve estimator efficiency.

The method is effective for multidimensional Markov random walks.

The approach provides a versatile tool for rare event probability estimation.

Abstract

Sequential Monte Carlo methods which involve sequential importance sampling and resampling are shown to provide a versatile approach to computing probabilities of rare events. By making use of martingale representations of the sequential Monte Carlo estimators, we show how resampling weights can be chosen to yield logarithmically efficient Monte Carlo estimates of large deviation probabilities for multidimensional Markov random walks.