Limit theorems for multifractal products of random fields

DOI10.1016/J.JMAA.2023.127888arXiv2202.02885OpenAlexW4387911459MaRDI QIDQ6390310

Illia Donhauzer, Andriy Olenko

Publication date: 6 February 2022

Abstract: This paper investigates asymptotic properties of multifractal products of random fields. The obtained limit theorems provide sufficient conditions for the convergence of cumulative fields in the spaces $L_q.$ New results on the rate of convergence of cumulative fields are presented. Simple unified conditions for the limit theorems and the calculation of the R'enyi function are given. They are less restrictive than those in the known one-dimensional results. The developed methodology is also applied to multidimensional multifractal measures. Finally, a new class of examples of geometric $varphi$-sub-Gaussian random fields is presented. In this case, the general assumptions have a simple form and can be expressed in terms of covariance functions only.

Full work available at URL: https://doi.org/10.1016/j.jmaa.2023.127888

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Random measures (60G57) Fractals (28A80)

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