On Exponential Limit Laws for Hitting Times of Rare Sets for Harris Chains and Processes
P. W. Glynn
J. Appl. Prob. Spec. Vol.48A, 319-326 (2011)
This paper provides a simple proof for the fact that the hitting time to an infrequently visited subset for a one-dependent regenerative process converges weakly to an exponential distribution. Special cases are positive recurrent Harris chains and Harris processes. The paper further extends this class of limit theorems to ``rewards'' that are cumulated to the hitting time of such a rare set.