First passage time distribution and the number of returns for ultrametric random walks

Abstract

In this paper, we consider a homogeneous Markov process ξ(t; ω) on an ultrametric space Qp, with distribution density f(x, t), x ∊ Qp, t ∊ R+, satisfying the equation , usually called the ultrametric diffusion equation. We construct and examine a random variable 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.