International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 2, Pages 373-380
doi:10.1155/S0161171287000437

Some limit theorems for ratios of transition probabilities

Abstract

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.