Limit Theorems for Multifractal Products of Geometric Stationary Processes

Denis Denisov; Nikolai Leonenko

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arXiv · 1110.2428

Limit Theorems for Multifractal Products of Geometric Stationary Processes

Denis Denisov·Nikolai Leonenko

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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 $L_q$ convergence of cumulative processes to the limiting processes and investigate their $q$-th order moments and Rényi functions, which are nonlinear, 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.

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BibTeX RIS

Denis Denisov, Nikolai Leonenko. 2015-05-11. Limit Theorems for Multifractal Products of Geometric Stationary Processes. https://arxiv.org/abs/1110.2428

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