Discretization of the Lamperti representation of a positive self-similar Markov process
| Autor: | Jakob D. Thøstesen, Jevgenijs Ivanovs |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Discretization Markov process Lamperti representation 01 natural sciences Lévy process Stable Lévy process conditioned to stay positive 010104 statistics & probability symbols.namesake Exponential functional Mathematics::Probability FOS: Mathematics Applied mathematics Positive self-similar Markov process 60G18 60G51 60F17 Limit (mathematics) 0101 mathematics Mathematics Applied Mathematics 010102 general mathematics Probability (math.PR) Representation (systemics) Scaling limit Modeling and Simulation symbols Small time behavior Mathematics - Probability |
| Zdroj: | Ivanovs, J & Thøstesen, J D 2021, ' Discretization of the Lamperti representation of a positive self-similar Markov process ', Stochastic Processes and Their Applications, vol. 137, pp. 200-221 . https://doi.org/10.1016/j.spa.2021.03.013 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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