On the scheme of rare events for a homogeneous Markov chain
The paper is concerned with a discrete-time Markov chain which is stopped as soon as a transition from a specific set of ``rare'' transitions occurs for the \(l\)th time. By letting the probabilities of the rare transitions tend to zero in a suitable way, an asymptotic result is obtained for the vector representing the number of transitions from each state until the chain is stopped. Also, a generalization of this result to semi-Markov processes is presented.
scientific article; zbMATH DE number 1529957