Asymptotic behaviour for critical slowing-down random walks
Statistical Mechanics
2015-06-24 v1 Probability
Exactly Solvable and Integrable Systems
Abstract
The jump processes W(t) on [0,\infty[ with transitions w -> alpha w at rate b*w^beta (0 =< alpha =< 1, b>0, beta>0) are considered. Their moments are shown to decay not faster than algebraically for t -> \infty, and an equilibrium probability density is found for a rescaled process U = (t + k)^{-beta} W. A corresponding birth process is discussed.
Cite
@article{arxiv.cond-mat/0012411,
title = {Asymptotic behaviour for critical slowing-down random walks},
author = {Yves Elskens},
journal= {arXiv preprint arXiv:cond-mat/0012411},
year = {2015}
}
Comments
8 pages, 4 figures Brussels 1999 (G. Nicolis festschrift) invited talk