Journal of Applied Probability

Approximating multivariate tempered stable processes

Boris Baeumer and Mihály Kovács

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Abstract

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

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

Dates
First available in Project Euclid: 8 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1331216840

Digital Object Identifier
doi:10.1239/jap/1331216840

Mathematical Reviews number (MathSciNet)
MR2952888

Zentralblatt MATH identifier
1248.60051

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

Keywords
Tempered stable process simulation Lévy process operator stable process spectral measure

Citation

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


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