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Return times for Stochastic processes with power-law scaling

Piero Olla
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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.

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BibTeXRIS

Piero Olla. 2007-07-30. Return times for Stochastic processes with power-law scaling. https://doi.org/10.1103/physreve.76.011122

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