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Dickman type stochastic processes with short- and long- range dependence

Year: 2025
Type: article
Abstract: 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.
Source: Stochastics
DOI: 10.1080/17442508.2025.2522789
Language: English
Open Access status: hybrid
Funders: London Mathematical Society, Cardiff University, Fundação de Amparo à Pesquisa do Estado de São Paulo, Hrvatska Zaklada za Znanost, Engineering and Physical Sciences Research Council, Australian Research Council, Division of Mathematical Sciences
Awards: Isaac Newton Institute for Mathematical Sciences (INI), G2203179303, Random fields: non-Gaussian stochastic models and approximation schemes, Fractional differential systems and stochastic, G3341554066, Isaac Newton Institute for Mathematical Sciences, G6852659267, G7503258488, Scaling in stochastic models
OpenAlex ID: W4411738587
FWCI: 3.997
Cites: 58
Cited by: 5
Related to: 10