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

Jevgenijs Ivanovs; Jakob D. Thøstesen

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arXiv · 2006.09115

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

Jevgenijs Ivanovs·Jakob D. Thøstesen

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Abstract

This paper considers discretization of the L\'evy 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 L\'evy 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 L\'evy processes conditioned to stay positive.

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BibTeX RIS

Jevgenijs Ivanovs, Jakob D. Thøstesen. 2020-06-16. Discretization of the Lamperti representation of a positive self-similar Markov process. https://arxiv.org/abs/2006.09115

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