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Approximating Multivariate Tempered Stable Processes

  • Boris Baeumer (a1) and Mihály Kovács (a1)
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.

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Corresponding author
Postal address: Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin, New Zealand.
∗∗ Email address: bbaeumer@maths.otago.ac.nz
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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