Limit Theorems for Multifractal Products of Geometric Stationary Processes

Denis Denisov, Nikolai Leonenko

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    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.
    Original languageEnglish
    Pages (from-to) 2579-2608
    Issue number4
    Publication statusPublished - 3 May 2016


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