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

Jevgenijs Ivanovs, Jakob D. Thøstesen*

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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.

OriginalsprogEngelsk
TidsskriftStochastic Processes and Their Applications
Vol/bind137
Sider (fra-til)200-221
Antal sider22
ISSN0304-4149
DOI
StatusUdgivet - jul. 2021

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