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Discretization of the Lamperti representation of a positive self-similar Markov process

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  • Ivanovs, Jevgenijs
  • Thøstesen, Jakob D.

Abstract

This paper considers discretization of the Lévy process appearing in the Lamperti representation of a strictly positive self-similar Markov process. Limit theorems for the resulting approximation are established under some regularity assumptions on the given Lévy process. Additionally, the scaling limit of a positive self-similar Markov process at small times is provided. Finally, we present an application to simulation of self-similar Lévy processes conditioned to stay positive.

Suggested Citation

  • Ivanovs, Jevgenijs & Thøstesen, Jakob D., 2021. "Discretization of the Lamperti representation of a positive self-similar Markov process," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 200-221.
    • Handle: RePEc:eee:spapps:v:137:y:2021:i:c:p:200-221
    DOI: 10.1016/j.spa.2021.03.013
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    References listed on IDEAS

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    1. Mark Podolskij & Mathias Vetter, 2010. "Understanding limit theorems for semimartingales: a short survey," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(3), pages 329-351, August.
    2. Mark Podolskij & Mathias Vetter, 2010. "Understanding limit theorems for semimartingales: a short survey," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 329-351.
    3. Søren Asmussen & Jevgenijs Ivanovs, 2018. "Discretization error for a two-sided reflected Lévy process," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 199-212, June.
    4. Bertoin, Jean, 1993. "Splitting at the infimum and excursions in half-lines for random walks and Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 47(1), pages 17-35, August.
    5. P. Salminen & L. Vostrikova, 2016. "On exponential functionals of processes with independent increments," Papers 1610.08732, arXiv.org, revised Mar 2018.
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