International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 373-380
Some limit theorems for ratios of transition probabilities
Department of Mathematics, Eastern Michigan University, Ypsilanti 48197, MI, USA
Received 8 October 1986
Copyright © 1987 Rita Chattopadhyay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, infinite dimensional forward convergent stochastic chains have been considered in the framework of . The main result of this paper deals with the observation that the total flow of probability from the -states to the -states is very small compared to that from the -states to the -states, if the chain is observed for a sufficiently long time. Some examples have been given to justify the assumptions involved.