First Passage Time Distribution and Number of Returns for Ultrametric Random Walk

Details First Passage Time Distribution and Number of Returns for Ultrametric Random Walk First Passage Time Distribution and Number of Returns for Ultrametric Random Walk

2008-08-22

arxiv.org/abs/0808.3066v1

Physics

Mathematical Physics

20 pages

Scientific paper

10.1088/1751-8113/42/8/085003

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.

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