Limit theorems for multifractal products of geometric stationary processes

Denisov, Denis and Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 2016. Limit theorems for multifractal products of geometric stationary processes. Bernoulli 22 (4) , pp. 2579-2608. 10.3150/15-BEJ738

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Abstract

We investigate the properties of multifractal products of geometric Gaussian processes with possible long-range dependence and geometric Ornstein–Uhlenbeck processes driven by Lévy motion and their finite and infinite superpositions. We present the general conditions for the Lq convergence of cumulative processes to the limiting processes and investigate their qth order moments and Rényi functions, which are non-linear, hence displaying the multifractality of the processes as constructed. We also establish the corresponding scenarios for the limiting processes, such as log-normal, log-gamma, log-tempered stable or log-normal tempered stable scenarios.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Bernoulli Society for Mathematical Statistics and Probability
ISSN:	1350-7265
Date of First Compliant Deposit:	9 May 2019
Date of Acceptance:	15 July 2015
Last Modified:	16 Nov 2024 03:15
URI:	https://orca.cardiff.ac.uk/id/eprint/89601

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