Journal of Applied Probability

Approximating multivariate tempered stable processes

Boris Baeumer and Mihály Kovács

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We give a simple method to approximate multidimensional exponentially tempered stable processes and show that the approximating process converges in the Skorokhod topology to the tempered process. The approximation is based on the generation of a random angle and a random variable with a lower-dimensional Lévy measure. We then show that if an arbitrarily small normal random variable is added, the marginal densities converge uniformly at an almost linear rate, providing a critical tool to assess the performance of existing particle tracking codes.

Article information

J. Appl. Probab., Volume 49, Number 1 (2012), 167-183.

First available in Project Euclid: 8 March 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G51: Processes with independent increments; Lévy processes
Secondary: 60G52: Stable processes

Tempered stable process simulation Lévy process operator stable process spectral measure


Baeumer, Boris; Kovács, Mihály. Approximating multivariate tempered stable processes. J. Appl. Probab. 49 (2012), no. 1, 167--183. doi:10.1239/jap/1331216840.

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