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On Approximation of Some Lévy Processes

Authors

  • Dmytro Ivanenko
  • Victoria Knopova Kyiv Taras Shevcjenko National University
  • Denis Platonov

Abstract

 In this paper, we extend the Asmussen-Rosinski approach for the approximation of Levy processes. To simulate the value of the process at time t, we introduce a time-dependent truncation of the Levy measure, which we refer to as dynamic cutting, followed by the simulation of the large-jump component. We provide the sufficient condition under which the compensated small-jump part can be replaced by a Gaussian approximation. We also derive weak approximation rates for both approaches. Finally, we run numerical simulations and compare the performance of our method with the Asmussen-Rosinski approach.

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How to Cite

Ivanenko, D., Knopova, V., & Platonov, D. On Approximation of Some Lévy Processes. Austrian Journal of Statistics, 54(1), 177–199. Retrieved from https://ajs.or.at/index.php/ajs/article/view/1991

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Section

Special Issue Department of Probability, Statistics and Actuarial Mathematics at TSNU of Kyiv