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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:137

Article

Ivanovs, Jevgenijs¹  Thostesen, Jakob D.¹ 

[1] Aarhus Univ, Dept Math, Ny Munkegade 118, DK-8000 Aarhus C, Denmark

关键词: Exponential functional;    Lamperti representation;    Positive self-similar Markov process;    Small time behavior;    Stable Levy process conditioned to stay positive;   

DOI  :  10.1016/j.spa.2021.03.013

来源: Elsevier

【 摘 要 】

This paper considers discretization of the Levy 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 Levy 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 Levy processes conditioned to stay positive. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free