A Note on Random Walks with Absorbing barriers and Sequential Monte Carlo Methods

Pierre del Moral (1) , Ajay Jasra (2)

1 CQFD - Quality control and dynamic reliability
2 NUS - National University of Singapore

In this article we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of 1-dimensional random walks with absorbing barriers. In particular, we develop a very precise variance analysis for several IS and SMC procedures. We take advantage of some explicit spectral formulae available for these models to derive sharp and explicit estimates; this provides stability properties of the associated normalized Feynman-Kac semigroups. Our analysis allows one to compare the variance of SMC and IS techniques for these models. The work in this article, is one of the few to consider an in-depth analysis of an SMC method for a particular model-type as well as variance comparison of SMC algorithms.

Mots clés: Sequential Monte Carlo; Feynman-Kac semigroups; Random walks with absorbing barriers; quasi-invariant measures; Importance Sampling; Particle samplers

Domaines: Probabilités [math.PR]

Pierre del Moral, Ajay Jasra. A Note on Random Walks with Absorbing barriers and Sequential Monte Carlo Methods. [Research Report] Arxiv. 2016. ⟨hal-01593874⟩