Discretization Of The Lamperti Representation Of A Positive Self-Similar Markov Process

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.