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Multifractality of products of geometric Ornstein-Uhlenbeck-type processes

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

V. V. Anh ,
Nikolai N. Leonenko  and
Narn-Rueih Shieh
V. V. Anh*
Affiliation:
Queensland University of Technology
Nikolai N. Leonenko*
Affiliation:
Cardiff University
Narn-Rueih Shieh*
Affiliation:
National Taiwan University
*
∗ Postal address: School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia. Email address: v.anh@qut.edu.au
∗∗ Postal address: Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4YH, UK. Email address: leonenkon@cardiff.ac.uk
∗∗∗ Postal address: Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan. Email address: shiehnr@math.ntu.edu.tw
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Abstract

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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.

Keywords

Multifractal productslong-range dependencegeometric Ornstein-Uhlenbeck processLévy processinfinitely divisible distribution

MSC classification

Primary: 60G57: Random measures 60G10: Stationary processes 60G17: Sample path properties
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 4 , December 2008 , pp. 1129 - 1156
Copyright
Copyright © Applied Probability Trust 2008 

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