Return times for Stochastic processes with power-law scaling

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.

9 pages, 5 figures, revtex4

References in corpus (9)

• The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory
• Recurrence time analysis, long-term correlations, and extreme events
• Multiscale velocity correlations in turbulence
• Mimicking a turbulent signal: sequential multiaffine processes
• Multifractal properties of return time statistics
• Expansion Around the Mean-Field Solution of the Bak-Sneppen Model
• Distribution of Return Intervals of Extreme Events
• Dual Multifractal Spectra
• Some relations between Lagrangian models and synthetic random velocity fields

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