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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 Hindawi Publishing Corporation. 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 [1]. The main result of this paper deals with the observation that the total flow of probability from the C-states to the T-states is very small compared to that from the T-states to the C-states, if the chain is observed for a sufficiently long time. Some examples have been given to justify the assumptions involved.