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

Abstract

In this paper, we consider a homogeneous Markov process ξ(t;ω) 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 τ(ω) 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.

20 pages

References in corpus (3)

• p-Adic Models of Ultrametric Diffusion Constrained by Hierarchical Energy Landscapes
• Application of p-adic analysis to models of spontaneous breaking of the replica symmetry
• p-Adic description of characteristic relaxation in complex systems

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