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• W33565650 abstract "Infinitely divisible random vectors and Lévy processes without Gaussian component admit representations with shot noise series. To enhance efficiency of the series representation in Monte Carlo simulations, we discuss variance reduction methods, such as stratified sampling, control variates and importance sampling, applied to exponential interarrival times forming the shot noise series. We also investigate the applicability of the generalized linear transformation method in the quasi-Monte Carlo framework to random elements of the series representation. Although implementation of the proposed techniques requires a small amount of initial work, the techniques have the potential to yield substantial improvements in estimator efficiency, as the plain use of the series representation in those frameworks is often expensive. Numerical results are provided to illustrate the effectiveness of our approaches.Keywordsquasi-Monte Carlo (QMC)Series RepresentationQMC MethodVariance Reduction MethodsImportance SamplingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
• W33565650 created "2016-06-24" @default.
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• W33565650 date "2012-01-01" @default.
• W33565650 modified "2023-09-25" @default.
• W33565650 title "On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws" @default.
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• W33565650 doi "https://doi.org/10.1007/978-3-642-27440-4_26" @default.
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