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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.

TidsskriftStochastic Processes and Their Applications
Sider (fra-til)200-221
Antal sider22
StatusUdgivet - jul. 2021

Bibliografisk note

Funding Information:
The authors gratefully acknowledge financial support of Sapere Aude Starting Grant 8049-00021B “Distributional Robustness in Assessment of Extreme Risk” from Independent Research Fund Denmark .

Publisher Copyright:
© 2021 Elsevier B.V.

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