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Intermittency of Superpositions of Ornstein–Uhlenbeck Type Processes

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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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Acknowledgments

N. Leonenko: This work has been supported in part by projects MTM2012-32674 (co-funded by European Regional Development Funds), and MTM2015-71839-P, MINECO, Spain. This research was also supported under Australian Research Council’s Discovery Projects funding scheme (Project Number DP160101366), and under Cardiff Incoming Visiting Fellowship Scheme and International Collaboration Seedcorn Fund.

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Authors and Affiliations

  1. Department of Mathematics, University of Osijek, 31000, Osijek, Croatia

    Danijel Grahovac

  2. Cardiff School of Mathematics, Cardiff University, Cardiff, CF24 4AG, UK

    Nikolai N. Leonenko

  3. Department of Statistics and Probability, Michigan State University, East Lansing, MI, 48824, USA

    Alla Sikorskii & Irena Tešnjak

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  1. Danijel Grahovac
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  2. Nikolai N. Leonenko
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  3. Alla Sikorskii
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  4. Irena Tešnjak
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Correspondence to Nikolai N. Leonenko.

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Grahovac, D., Leonenko, N.N., Sikorskii, A. et al. Intermittency of Superpositions of Ornstein–Uhlenbeck Type Processes. J Stat Phys 165, 390–408 (2016). https://doi.org/10.1007/s10955-016-1616-7

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  • DOI: https://doi.org/10.1007/s10955-016-1616-7

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