Jo luettua : intertekstuaalisuus kulttuuriteoriana tai metodina?

Lehtonen, Tuomas M. S.

doi:10.51809/te.104241

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Introduction Among Variance Reduction Techniques For Efficie...1

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2005

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“…The first result of this type was given by Siegmund [34]. The basic idea was subsequently investigated in many contexts, and a small selection of the literally hundreds of papers on the topics is [ [1,2,3,7,8,9], [11,12,15,17,18,20,24,25,29,30,33]]. Necessary and sufficient conditions under which a prescribed scheme is asymptotically optimal are discussed in [10,31,32], while [21] gives a survey of rare-event simulation.…”

Section: Introduction Among Variance Reduction Techniques For Efficie...mentioning

confidence: 99%

Dynamic importance sampling for uniformly recurrent Markov chains

Dupuis¹,

Wang²

2005

Ann. Appl. Probab.

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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.

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