Limit Theorems for Multifractal Products of Geometric Stationary\n Processes

2011/10/11 by Denis Denisov, Nikolai Leonenko, Denisov, Denis +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1110.2428

Abstract

We investigate the properties of multifractal products of geometric Gaussian\nprocesses with possible long-range dependence and geometric Ornstein-Uhlenbeck\nprocesses driven by L 'evy motion and their finite and infinite\nsuperpositions. We present the general conditions for the L_q convergence of\ncumulative processes to the limiting processes and investigate their q-th\norder moments and R 'enyi functions, which are nonlinear, hence displaying\nthe multifractality of the processes as constructed. We also establish the\ncorresponding scenarios for the limiting processes, such as log-normal,\nlog-gamma, log-tempered stable or log-normal tempered stable scenarios.\n

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• Infinite Dimensional Multifractal Analysis of the Wiener measure
• Asymptotics of multifractal products of spherical random fields

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