Long-range correlated stationary Markovian processes
Statistical Mechanics
2007-05-23 v1
Abstract
We introduce a new class of stochastic processes which are stationary, Markovian and characterized by an infinite range of time-scales. By transforming the Fokker-Planck equation of the process into a Schrodinger equation with an appropriate quantum potential we determine the asymptotic behavior of the autocorrelation function of the process in an analytical way. We find the conditions needed to observe a stationary long-range correlated Markovian process. In the presence of long-range correlation, for selected values of the control parameters, the process has a 1/f-like spectral density for low frequency values.
Cite
@article{arxiv.cond-mat/0203442,
title = {Long-range correlated stationary Markovian processes},
author = {Fabrizio Lillo and Salvatore Micciche' and Rosario N. Mantegna},
journal= {arXiv preprint arXiv:cond-mat/0203442},
year = {2007}
}
Comments
4 pages