On simulation of tempered stable random variates

Reiichiro Kawai, Hiroki Masuda

    Research output: Contribution to journalArticlepeer-review

    50 Citations (Scopus)

    Abstract

    Various simulation methods for tempered stable random variates with stability index greater than one are investigated with a view towards practical implementation, in particular cases of very small scale parameter, which correspond to increments of a tempered stable Lvy process with a very short stepsize. Methods under consideration are based on acceptancerejection sampling, a Gaussian approximation of a small jump component, and infinite shot noise series representations. Numerical results are presented to discuss advantages, limitations and trade-off issues between approximation error and required computing effort. With a given computing budget, an approximative acceptancerejection sampling technique Baeumer and Meerschaert (2009) [11] is both most efficient and handiest in the case of very small scale parameter and moreover, any desired level of accuracy may be attained with a small amount of additional computing effort.

    Original languageEnglish
    Pages (from-to)2873-2887
    Number of pages15
    JournalJournal of Computational and Applied Mathematics
    Volume235
    Issue number8
    DOIs
    Publication statusPublished - Feb 15 2011

    All Science Journal Classification (ASJC) codes

    • Computational Mathematics
    • Applied Mathematics

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