Intermittency of Superpositions of Ornstein-Uhlenbeck Type Processes

Danijel Grahovac; Nikolai N. Leonenko; Alla Sikorskii; Irena Tešnjak

doi:10.1007/s10955-016-1616-7

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arXiv · 1512.00670

Intermittency of Superpositions of Ornstein-Uhlenbeck Type Processes

Danijel Grahovac·Nikolai N. Leonenko·Alla Sikorskii·Irena Tešnjak

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Abstract

The phenomenon of intermittency has been widely discussed in physics literature. This paper provides a model of intermittency based on Lévy driven Ornstein-Uhlenbeck (OU) type processes. Discrete superpositions of these processes can be constructed to incorporate non-Gaussian marginal distributions and long or short range dependence. While the partial sums of finite superpositions of OU type processes obey the central limit theorem, we show that the partial sums of a large class of infinite long range dependent superpositions are intermittent. We discuss the property of intermittency and behavior of the cumulants for the superpositions of OU type processes.

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Danijel Grahovac, Nikolai N. Leonenko, Alla Sikorskii, Irena Tešnjak. 2015-12-02. Intermittency of Superpositions of Ornstein-Uhlenbeck Type Processes. https://doi.org/10.1007/s10955-016-1616-7

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