Imperfect surveillance schemes for detecting a change in the distribution of a stationary process. the markovian case

Abstract

Let be a stationary stochastic process with distribution P. We consider the problem of detecting a change in distribution from Pto a specified Q. We further assume that the process may not be continuously observed; thus we study the relevant design problem of choosing the observational instants.

Asymptotics of operational characteristics of cusum procedures are obtained, for natural designs, in the case where {x_t} is a 0-1 continuous time Markov process under P and Q. The asymptotics is based on a Brownian motion approximation of a Markov process.