Large deviation property of waiting times for Markov and mixing processes
Vatsal Sharan, Rakesh K Bansal · 2014
In this work, we study the asymptotic properties of the waiting time until the opening string in the realization of a process first appears in an independent realization of the same or a different process. We first establish that the normalized waiting time between two independent realizations of a single source obeys the large deviation property for a class of mixing processes. Using the method of Markov types, we extend the result to when both the sequences are realizations of two distinct irreducible and aperiodic Markov sources.