Simulation of supOU processes with specified marginal distribution and correlation function

Leonenko, Nikolai N.; Pepelyshev, Andrey

doi:10.15559/25-VMSTA291

Modern Stochastics: Theory and Applications

Simulation of supOU processes with specified marginal distribution and correlation function

Nikolai N. Leonenko

Andrey Pepelyshev

https://doi.org/10.15559/25-VMSTA291

Pub. online: 15 January 2026 Type: Research Article

Open Access

Received
18 September 2025

Revised
8 December 2025

Accepted
29 December 2025

Published
15 January 2026

Abstract

An algorithm is proposed for simulation of superpositions of Ornstein–Uhlenbeck processes which may have short- or long-range dependencies and specified marginal distributions. The algorithm is based on the Bondesson–Rosinski representation of the supOU process as a shot-noise process and enables a clear constructive view on the structure of supOU processes. The use of the proposed algorithm is demonstrated for eight positive marginal distributions and eight entire real line marginal distributions when the explicit formulae for the Lévy density are available or not.

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Keywords

Ornstein–Uhlenbeck process self-decomposable distribution long-range dependence Lévy basis shot-noise process

MSC2020

60G10 65C05

Funding

Nikolai Leonenko (NL) would like to thank for support and hospitality during the programmes “Fractional Differential Equations” (FDE2), “Uncertainly Quantification and Modelling of Materials” (USM), both supported by EPSRC grant EP/R014604/1, and the programme “Stochastic systems for anomalous diffusion” (SSD), supported by EPSRC grant EP/Z000580/1, at Isaac Newton Institute for Mathematical Sciences, Cambridge. Also, NL was partially supported under the ARC Discovery Grant DP220101680 (Australia), Croatian Scientific Foundation (HRZZ) grant “Scaling in Stochastic Models” (IP-2022-10-8081), grant FAPESP 22/09201-8 (Brazil) and the Taith Research Mobility grant (Wales, Cardiff University).

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