On the distribution of the hitting time for the N-urn Ehrenfest model

TL;DR

This paper derives explicit formulas for the Laplace transform and moments of hitting times in the N-urn Ehrenfest model using an auxiliary continuous-time Markov chain, advancing understanding of its stochastic behavior.

Contribution

It introduces a method to compute the Laplace transform and high-order moments of hitting times in the N-urn Ehrenfest model using an auxiliary continuous-time Markov chain.

Findings

Explicit Laplace transform formula for hitting times

High-order moments, including variance, computed for the model

Applicable to symmetric state sets in the Ehrenfest process

Abstract

In this paper, we consider the N-urn Ehrenfest model. By utilizing an auxiliary continuous-time Markov chain, we obtain the explicit formula for the Laplace transform of the hitting time from a single state to a set A of states where A satisfies some symmetric properties. After obtaining the Laplace transform, we are able to compute the high-order moments(especially, variance) for the hitting time.