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Rare Event Monte Carlo and Importance Sampling

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Part of the Probability Theory and Stochastic Modelling book series (PTSM,volume 94)

Abstract

Suppose that in the analysis of some system, the value of a probability or expected value that is largely determined by one or a few events is important. Examples include the data loss in a communication network; depletion of capital reserves in a model for insurance; motion between metastable states in a chemical reaction network; and exceedance of a regulatory threshold in a model for pollution in a waterway. In previous chapters we have described how large deviation theory gives approximations for such quantities. The approximations take the form of logarithmic asymptotics, i.e., exponential decay rates.

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  • DOI: 10.1007/978-1-4939-9579-0_14
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Notes

  1. 1.

    For certain special structures one can obtain more accurate approximations, e.g., approximations which identify both the exponential rate of decay as well as “pre-exponential” terms.

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Correspondence to Amarjit Budhiraja .

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Budhiraja, A., Dupuis, P. (2019). Rare Event Monte Carlo and Importance Sampling. In: Analysis and Approximation of Rare Events. Probability Theory and Stochastic Modelling, vol 94. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9579-0_14

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