On a Class of Markov Processes Taking Values on Lines and the Central Limit Theorem

Abstract

We shall consider a class of Markov processes (n(t), x(t)) with the continuous time parameter t∈e[0, ∞), whose state space is {1, 2,..., N}×R¹. We shall assume that the processes are spacially homogeneous with respect to X∈R¹. In detail, our assumption is that the transition functionF_ij(x,t) = P(n(t) = j, x(t)≦x|n(0) = i,x(0) = 0), t > 0, 1≦i, j,≦N, x∈R¹satisfies following conditions (1, 1)~(1,4).