Dickman type stochastic processes with short- and long- range dependence
Probability
2025-06-19 v2 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.2408.11521,
title = {Dickman type stochastic processes with short- and long- range dependence},
author = {Danijel Grahovac and Anastasiia Kovtun and Nikolai N. Leonenko and Andrey Pepelyshev},
journal= {arXiv preprint arXiv:2408.11521},
year = {2025}
}
Comments
24 pages, 3 figures