Surprise probabilities in Markov chains

In a Markov chain started at a state x, the hitting time τ(y) is the first time that the chain reaches another state y. We study the probability Px(τ(y) = t) that the first visit to y occurs precisely at a given time t. Informally speaking, the event that a new state is visited at a large time t may be considered a \"surprise\". We prove ...More