First Passage Time Distribution and Number of Returns for Ultrametric Random Walk
Mathematical Physics
2009-11-13 v1 math.MP
Abstract
In this paper, we consider a homogeneous Markov process \xi(t;\omega) on an ultrametric space Q_p, with distribution density f(x,t), x in Q_p, t in R_+, satisfying the ultrametric diffusion equation df(x,t)/dt =-Df(x,t). We construct and examine a random variable \tau (\omega) that has the meaning the first passage times. Also, we obtain a formula for the mean number of returns on the interval (0,t] and give its asymptotic estimates for large t.
Keywords
Cite
@article{arxiv.0808.3066,
title = {First Passage Time Distribution and Number of Returns for Ultrametric Random Walk},
author = {V. A. Avetisov and A. Kh. Bikulov and A. P. Zubarev},
journal= {arXiv preprint arXiv:0808.3066},
year = {2009}
}
Comments
20 pages