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

Grahovac, Danijel, Kovtun, Anastasiia, Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091 and Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559 2025. Dickman type stochastic processes with short- and long- range dependence. Stochastics: An International Journal of Probability and Stochastic Processes 10.1080/17442508.2025.2522789

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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.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Schools > Mathematics
Additional Information:	License information from Publisher: LICENSE 1: URL: http://creativecommons.org/licenses/by-nc-nd/4.0/, Start Date: 2025-06-27
Publisher:	Taylor and Francis Group
ISSN:	1744-2508
Date of First Compliant Deposit:	10 July 2025
Date of Acceptance:	17 June 2025
Last Modified:	10 Jul 2025 15:45
URI:	https://orca.cardiff.ac.uk/id/eprint/179720

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