Quickest detection of an accumulated state-dependent change point

Abstract

Motivated by the practical investigation of a state-dependent quickest detection problem in continuous time, especially for Brownian observations, we propose an asymptotic scheme in discrete time called a quickest detection scheme of an accumulated state-dependent change point. Here the state-dependent means that the priori probability of the change point depends on the current state. We reduce the problem to finding an optimal stopping time of a vector-valued Markov process. We illustrate the scheme via a numerical example.