Intermittency of Superpositions of Ornstein-Uhlenbeck Type Processes

TL;DR

This paper models intermittency using superpositions of Lévy-driven Ornstein-Uhlenbeck processes, revealing that infinite superpositions exhibit intermittent behavior with implications for understanding complex stochastic phenomena.

Contribution

It introduces a framework for modeling intermittency through infinite superpositions of OU processes with non-Gaussian distributions and dependence structures.

Findings

Finite superpositions follow the central limit theorem

Infinite superpositions display intermittency

Cumulant behavior analyzed for superpositions

Abstract

The phenomenon of intermittency has been widely discussed in physics literature. This paper provides a model of intermittency based on L\'evy 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.