Multifractality of products of geometric Ornstein-Uhlenbeck-type processes
Resource
Advances in Applied Probability 40 (4): 1129-1156
Journal
Advances in Applied Probability
Pages
1129-1156
Date Issued
2008
Date
2008
Author(s)
Anh, Vo V.
Leonenko, Nikolai N.
Shieh, Narn-Rueih
Abstract
We investigate the properties of multifractal products of geometric Ornstein-Uhlenbeck (OU) processes driven by L?vy 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 L?vy 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 R?nyi functions and dependence structure.
Type
journal article
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