Intermittency of Superpositions of Ornstein-Uhlenbeck Type Processes

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.

References in corpus (2)

• Multivariate supOU processes
• Intermittency and multifractality: A case study via parabolic stochastic PDEs

Cited by in corpus (7)

• Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes
• The almost-sure asymptotic behavior of the solution to the stochastic heat equation with Lévy noise
• Dickman type stochastic processes with short- and long- range dependence
• Intermittency and multiscaling in limit theorems
• Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein-Uhlenbeck processes
• Intermittency in the small-time behavior of Lévy processes
• Weak dependence and GMM estimation of supOU and mixed moving average processes