Dickman type stochastic processes with short- and long- range dependence
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912437133901824 |
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| author | Grahovac, Danijel Kovtun, Anastasiia Leonenko, Nikolai N. Pepelyshev, Andrey |
| author_facet | Grahovac, Danijel Kovtun, Anastasiia Leonenko, Nikolai N. Pepelyshev, Andrey |
| contents | We study properties of the (generalized) Dickman distribution with two parameters and the stationary solution of the Ornstein-Uhlenbeck stochastic differential equation driven by a Poisson process. In particular, we show that the marginal distribution of this solution is the Dickman distribution. Additionally, we investigate superpositions of Ornstein-Uhlenbeck processes which may have short- or long-range dependencies and marginal distribution of the form of the Dickman distribution. The numerical algorithm for simulation of these processes is presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11521 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dickman type stochastic processes with short- and long- range dependence Grahovac, Danijel Kovtun, Anastasiia Leonenko, Nikolai N. Pepelyshev, Andrey Probability Statistics Theory 60G10 We study properties of the (generalized) Dickman distribution with two parameters and the stationary solution of the Ornstein-Uhlenbeck stochastic differential equation driven by a Poisson process. In particular, we show that the marginal distribution of this solution is the Dickman distribution. Additionally, we investigate superpositions of Ornstein-Uhlenbeck processes which may have short- or long-range dependencies and marginal distribution of the form of the Dickman distribution. The numerical algorithm for simulation of these processes is presented. |
| title | Dickman type stochastic processes with short- and long- range dependence |
| topic | Probability Statistics Theory 60G10 |
| url | https://arxiv.org/abs/2408.11521 |