On a Class of Markov Processes Taking Values on Lines and the Central Limit Theorem
- 1 August 1967
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 30, 47-56
- https://doi.org/10.1017/s0027763000012344
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 functionFij(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).Keywords
This publication has 2 references indexed in Scilit:
- A central limit theorem for processes defined on a finite Markov chainMathematical Proceedings of the Cambridge Philosophical Society, 1964
- The Theory of Branching ProcessesPublished by Springer Nature ,1963