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On Simulation of Tempered Stable Random Variates

By Reiichiro Kawai and Hiroki Masuda


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 Lévy process with a very short stepsize. Methods under consideration are based on acceptance–rejection 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 acceptance–rejection 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

Topics: Acceptance–rejection sampling, Compound Poisson, Gaussian approximation, Infinite shot noise series, Tempered stable distribution, Characteristic function
Publisher: Elsevier
Year: 2010
DOI identifier: 10.1016/
OAI identifier:

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