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 out. 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 have been provided in the preasymptotic regime. 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.