Return times for Stochastic processes with power-law scaling

Details Return times for Stochastic processes with power-law scaling Return times for Stochastic processes with power-law scaling

2006-06-13

arxiv.org/abs/cond-mat/0606323v3

Phys. Rev. E Vol. 76, 011122 (2007)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 5 figures, revtex4

Scientific paper

10.1103/PhysRevE.76.011122

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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