2005/02/01 by Paul Dupuis, Hui Wang · 1 citation
Decision Sciences · Mathematics · Social Sciences · #Insurance, Mortality, Demography, Risk Management #Markov Chains and Monte Carlo Methods #Probability and Risk Models #math.PR #msc:60F10 #msc:65C05 #msc:93E20
paper · pdf · doi:10.1214/105051604000001016
published as Annals of Applied Probability 2005, Vol. 15, No. 1A, 1-38 · Published at http://dx.doi.org/10.1214/105051604000001016 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2005/02/01 · arxiv created 2005/03/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. In standard importance sampling schemes, the system is simulated using an a priori fixed change of measure suggested by a large deviation lower bound analysis. Recent work, however, has suggested that such schemes do not work well in many situations. In this paper we consider dynamic importance sampling in the setting of uniformly recurrent Markov chains. By “dynamic” we mean that in the course of a single simulation, the change of measure can depend on the outcome of the simulation up till that time. Based on a control-theoretic approach to large deviations, the existence of asymptotically optimal dynamic schemes is demonstrated in great generality. The implementation of the dynamic schemes is carried out with the help of a limiting Bellman equation. Numerical examples are presented to contrast the dynamic and standard schemes.