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Generation of Random Variates Using Asymptotic Expansions

  • Monte-Carlo methods are widely used numerical tools in various fields of application, like rarefied gas dynamics, vacuum technology, stellar dynamics or nuclear physics. A central part in all applications is the generation of random variates according to a given probability law. Fundamental techniques to generate non-uniform random variates are the inversion principle or the acceptance-rejection method. Both procedures can be quite time-consuming if the given probability law has a complicated structure.; In this paper we consider probability laws depending on a small parameter and investigate the use of asmptotic expansions to generate random variates. The results given in the paper are restrictedto first order expansions. We show error estimates for the discrepancy as well as for the bounded Lipschitz distance of the asymptotic expansion. Furthermore the integration error for some special classes of functions is given. The efficiency of the method is proved by a numerical example from rarefied gas flows.

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Author:Jens Struckmeier
URN (permanent link):urn:nbn:de:hbz:386-kluedo-5048
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (107)
Document Type:Preprint
Language of publication:English
Year of Completion:1994
Year of Publication:1994
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Random number generation; asymptotic expansions; inversion method
Source:Computing, Vol. 59, No. 4, 331-347 (1997)
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Exx Asymptotic theory / 34E05 Asymptotic expansions
65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C10 Random number generation
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011