Denisov, Denis and Leonenko, Nikolai
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 |
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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: | 29 Jun 2019 18:37 |
URI: | http://orca.cf.ac.uk/id/eprint/89601 |
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