Multiscaling limit theorems for stochastic FPDE with cyclic long-range dependence

Alghamdi, Maha Mosaad A, Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Olenko, Andriy 2025. Multiscaling limit theorems for stochastic FPDE with cyclic long-range dependence. Brazilian Journal of Probability and Statistics Item availability restricted.

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Abstract

The paper studies solutions of stochastic partial differential equations with random initial conditions. First, it overviews some of the known results on scaled solutions of such equations and provides several explicit motivating examples. Then, it proves multiscaling limit theorems for renormalized solutions for the case of initial conditions subordinated to random processes with cyclic long-range dependence. Two cases of stochastic partial differential equations are examined. The spectral and covariance representations for the corresponding limit random fields are derived. Additionally, it is discussed why analogous results are not valid for subordinated cases with Hermite ranks greater than 1. Numerical examples that illustrate the obtained theoretical results are presented.

Item Type:	Article
Status:	In Press
Schools:	Schools > Mathematics
Publisher:	Brazilian Statistical Society
ISSN:	0103-0752
Date of First Compliant Deposit:	26 May 2025
Date of Acceptance:	26 May 2025
Last Modified:	13 Jun 2025 11:45
URI:	https://orca.cardiff.ac.uk/id/eprint/178505

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