The general discrete time disorder problem

Abstract

In the classical discrete time disorder problem the goal is to detect, with minimum average delay, a change in the distribution of a sequence of IID random variables. In this paper the concept of a disorder is extended to an arbitrary filtration. The performance of a Markov time used to detect the disorder is measured using a general cost function. The expected value of the cost function is expressed as a nonanticipative function of the observations. Optimal stopping theory can then be used to determine a Markov time which minimizes the expected cost

Keywords:

• Disorder problem
• quickest detection
• Markov time
• optimal stopping