Return times for Stochastic processes with power-law scaling

TL;DR

This paper analytically investigates the return time distribution of extreme events in stochastic processes with power-law correlations, revealing stretched exponential scaling and discussing applicability to non-Gaussian and multifractal processes.

Contribution

It introduces an epsilon-expansion approach to derive analytical expressions for return time distributions in power-law correlated stochastic processes.

Findings

Return time distribution exhibits stretched exponential scaling.

Analytical expressions valid in the pre-asymptotic regime are provided.

Conditions for applying the theory to non-Gaussian processes are analyzed.

Abstract

An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried on. The calculation is based on an epsilon-expansion in the correlation exponent: C(t)=|t|^{-1+epsilon}. The fixed point of the theory is associated with stretched exponential scaling of the distribution; analytical expressions, valid in the pre-asymptotic regime, have been provided. Also the permanence time distribution appears to be characterized by stretched exponential scaling. The conditions for application of the theory to non-Gaussian processes have been analyzed and the relations with the issue of return times in the case of multifractal measures have been discussed.