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Multifractality of products of geometric Ornstein-Uhlenbeck-type processes

  • V. V. Anh (a1), Nikolai N. Leonenko (a2) and Narn-Rueih Shieh (a3)

Abstract

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.

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Copyright

Corresponding author

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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Multifractality of products of geometric Ornstein-Uhlenbeck-type processes

  • V. V. Anh (a1), Nikolai N. Leonenko (a2) and Narn-Rueih Shieh (a3)

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