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arXiv · 2408.11521

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

Danijel Grahovac·Anastasiia Kovtun·Nikolai N. Leonenko·Andrey Pepelyshev
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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.

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Danijel Grahovac, Anastasiia Kovtun, Nikolai N. Leonenko, Andrey Pepelyshev. 2024-08-21. Dickman type stochastic processes with short- and long- range dependence. https://doi.org/10.1080/17442508.2025.2522789

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