In this article we consider importance sampling (IS) and sequential MonteCarlo (SMC) methods in the context of 1-dimensional random walks with absorbingbarriers. In particular, we develop a very precise variance analysis forseveral IS and SMC procedures. We take advantage of some explicit spectralformulae available for these models to derive sharp and explicit estimates;this provides stability properties of the associated normalized Feynman-Kacsemigroups. Our analysis allows one to compare the variance of SMC and IStechniques for these models. The work in this article, is one of the few toconsider an in-depth analysis of an SMC method for a particular model-type aswell as variance comparison of SMC algorithms.
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