| In this thesis,we mainly study the N-Urn Ehrenfest Model.The model is consist of N urns and M balls.The urns are numbered from 1 to N,and the balls are numbered from 1 to M.The M balls are initially distributed in the N urns.At each time,choose a ball randomly and put it into another urn with equal probability.The average transfer time from that all the M balls being in No.1 urn to the first time that all the balls being in No.2 urn is calculated in some papers.But for some general questions such as the distribution and the mean of the hitting times,they are still open.Based on the previous results,this paper focus on the hitting times of the model.We introduce a continuous time Markov chain{Y(t);t ≥ 0} with the state space E =｛(x1,…,xM):1 ≤x1,…,xM ≤N} and its embedding Markov chain ｛Xn;n =0,1,2,…}.Here,{Xn;n = 0,1,2,…} characterize our model.For A(?)E,let TAX and TA be the first visiting to A with respect to ｛Xn} and to {Y(t)} respectively.We discuss the relationship about the means,variances and the generating functions between TAX and TA.We give the expression of the generating function of TA under certain conditions.When A is a single point set,we prove that the moments of TA is finite and give the recursive expressions of them.In the end,we compute the means of four special hitting times in {Xn}. |
