MULTIFRACTALITY OF PRODUCTS OF GEOMETRIC ORNSTEIN-UHLENBECK-TYPE PROCESSES

作者：Anh V V^*; Leonenko Nikolai N; Shieh Narn Rueih

来源：Advances in Applied Probability, 2008, 40(4): 1129-1156.

DOI：10.1239/aap/1231340167

• Multifractal products
• long-range dependence
• geometric Ornstein-Uhlenbeck process
• Levy process
• infinitely divisible distribution

We investigate the properties of multifractal products of geometric Ornstein-Uhlenbeck (OU) processes driven by Levy 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 Levy 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 Renyi functions and dependence structure.

• 出版日期2008-12