English

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

R2 v1 2026-06-21T11:12:57.688Z