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

Jevgenijs Ivanovs and Jakob D. Thøstesen

Stochastic Processes and their Applications, 2021, vol. 137, issue C, 200-221

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.

Keywords: Exponential functional; Lamperti representation; Positive self-similar Markov process; Small time behavior; Stable Lévy process conditioned to stay positive (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:137:y:2021:i:c:p:200-221

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DOI: 10.1016/j.spa.2021.03.013

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