Journal of Statistical Physics

, Volume 165, Issue 2, pp 390–408 | Cite as

Intermittency of Superpositions of Ornstein–Uhlenbeck Type Processes

  • Danijel Grahovac
  • Nikolai N. LeonenkoEmail author
  • Alla Sikorskii
  • Irena Tešnjak


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.


Ornstein–Uhlenbeck type processes Intermittency Long range dependence Weak convergence 

Mathematics Subject Classification

60F06 60G10 60G99 



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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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Danijel Grahovac
    • 1
  • Nikolai N. Leonenko
    • 2
    Email author
  • Alla Sikorskii
    • 3
  • Irena Tešnjak
    • 3
  1. 1.Department of MathematicsUniversity of OsijekOsijekCroatia
  2. 2.Cardiff School of MathematicsCardiff UniversityCardiffUK
  3. 3.Department of Statistics and ProbabilityMichigan State UniversityEast LansingUSA

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