On-line detection of a part of a sequence with unspecified distribution (Q951210)

A discrete time Markov process is observed. At two random moments \(\theta _{1}, \theta _{2}\), where \(\theta _{1}< \theta _{2}\), the distribution of the observed sequence changes. The distribution is assumed to be known before \(\theta _{1}\) and after \(\theta _{2}\), but between these instants is unknown, chosen randomly from a finite set of distributions. The optimal stopping rule for stopping the observations between the disorders \(\theta _{1}\) and \(\theta _{2}\) is identified.