A note on random walks with absorbing barriers and sequential Monte Carlo methods

作者：Del Moral Pierre; Jasra Ajay^*

来源：Stochastic Analysis and Applications, 2018, 36(3): 413-442.

DOI：10.1080/07362994.2017.1412264

• Random walks with absorbing barriers
• quasi-invariant measures
• importance sampling
• particle samplers
• sequential Monte Carlo
• Feynman-Kac semigroups
• Primary 82C80
• 60K35
• Secondary 60F99
• 62F15

In this article, we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of one-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.

• 出版日期2018
• 单位INRIA