AGGREGATED MARKOV-PROCESSES WITH NEGATIVE EXPONENTIAL TIME INTERVAL OMISSION

We consider a time reversible, continuous time Markov chain on a finite state space. The state space is partitioned into two sets, termed open and closed, and it is only possible to observe whether the process is in an open or a closed state. Further, short sojourns in either the open or closed states fail to be detected. We consider the situation when the length of minimal detectable sojourns follows a negative exponential distribution with mean mu-1. We show that the probability density function of observed open sojourns takes the form f(o)(t) = SIGMA-i = 1n alpha-approximatey i exp (lambda-approximately i(t)), where n is the size of the state space. We present a thorough asymptotic analysis of f(o)(t) as mu tends to infinity. We discuss the relevance of our results to the modelling of single channel records. We illustrate the theory with a numerical example.