Dickman type stochastic processes with short- and long- range dependence
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.
Authors
- Andrey Pepelyshev (ORCID: https://orcid.org/0000-0001-5634-5559)
- Danijel Grahovac (ORCID: https://orcid.org/0000-0001-6918-3456)
- Nikolai Leonenko (ORCID: https://orcid.org/0000-0003-1932-4091)
- Anastasiia Kovtun
Institutions
- University of Osijek (HR)
- Cardiff University (GB)
Publication Details
- Journal
- Stochastics
- Published
- 2025-06-27
- DOI
- https://doi.org/10.1080/17442508.2025.2522789
- Citations
- 3
- Primary Topic
- Stochastic processes and financial applications
- Type
- article
- Field-Weighted Citation Impact
- 6.62
Funders
- London Mathematical Society
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Hrvatska Zaklada za Znanost
- Engineering and Physical Sciences Research Council
- Australian Research Council