Stochastic processes with finite correlation time: modeling and application to the generalized Langevin equation
Statistical Mechanics
2009-11-07 v1
Abstract
The kangaroo process (KP) is characterized by various forms of the covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte Carlo method. Some results appear to be incompatible with requirements of the fluctuation-dissipation theorem because probability distributions change when the process is inserted into the equation. We demonstrate how one can construct a model of noise free of that difficulty. This form of the KP is especially suitable for physical applications.
Keywords
Cite
@article{arxiv.cond-mat/0101131,
title = {Stochastic processes with finite correlation time: modeling and application to the generalized Langevin equation},
author = {T. Srokowski},
journal= {arXiv preprint arXiv:cond-mat/0101131},
year = {2009}
}
Comments
22 pages (RevTeX) and 4 figures