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Jakob Dalsgaard Thøstesen

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

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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.

Original languageEnglish
JournalStochastic Processes and Their Applications
Pages (from-to)200-221
Number of pages22
Publication statusPublished - Jul 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

    Research areas

  • Exponential functional, Lamperti representation, Positive self-similar Markov process, Small time behavior, Stable Lévy process conditioned to stay positive

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