Multifractality of products of geometric Ornstein-Uhlenbeck-type processes

We investigate the properties of multifractal products of geometric Ornstein-Uhlenbeck (OU) processes driven by Lévy motion. The conditions on the mean, variance, and covariance functions of the resulting cumulative processes are interpreted in terms of the moment generating functions. We consider f...

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Bibliographic Details
Published in:Advances in applied probability 2008-12, Vol.40 (4), p.1129-1156
Main Authors: Anh, V. V., Leonenko, Nikolai N., Shieh, Narn-Rueih
Format: Article
Language:English
Subjects:
60G10
60G17
60G57
Covariance
Density
Eigenfunctions
General Applied Probability
Generating function
geometric Ornstein-Uhlenbeck process
infinitely divisible distribution
long-range dependence
Lévy process
Mathematical functions
Mathematical theorems
Multifractal products
Normal distribution
Probability
Random variables
Stationary processes
Stochastic models
Stochastic processes
Studies
Turbulence
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Summary:We investigate the properties of multifractal products of geometric Ornstein-Uhlenbeck (OU) processes driven by Lévy motion. The conditions on the mean, variance, and covariance functions of the resulting cumulative processes are interpreted in terms of the moment generating functions. We consider five cases of infinitely divisible distributions for the background driving Lévy processes, namely, the gamma and variance gamma distributions, the inverse Gaussian and normal inverse Gaussian distributions, and the z-distributions. We establish the corresponding scenarios for the limiting processes, including their Rényi functions and dependence structure.
ISSN:0001-8678
1475-6064
DOI:10.1239/aap/1231340167