A functional limit theorem for general shot noise processes
| Autor: | Iksanov, Alexander, Rashytov, Bohdan |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | J. Appl. Probab. 57 (2020) 280-294 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/jpr.2019.95 |
| Popis: | By a general shot noise process we mean a shot noise process in which the counting process of shots is arbitrary locally finite. Assuming that the counting process of shots satisfies a functional limit theorem in the Skorokhod space with a locally H\"{o}lder continuous Gaussian limit process and that the response function is regularly varying at infinity we prove that the corresponding general shot noise process satisfies a similar functional limit theorem with a different limit process and different normalization and centering functions. For instance, if the limit process for the counting process of shots is a Brownian motion, then the limit process for the general shot noise process is a Riemann-Liouville process. We specialize our result for five particular counting processes. Also, we investigate H\"{o}lder continuity of the limit processes for general shot noise processes. Comment: 15 pages, submitted to a journal |
| Databáze: | arXiv |
| Externí odkaz: |
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