Optimal detection of transition probability change in random sequence

Abstract

In this paper, we register a random sequence constructed based on Markov processes by switching between them. At unobservable random moment, a change in distribution of observed sequence takes place. Using probability maximizing approach, the optimal stopping rule for detecting the disorder is identified. Some explicit solution for example is also obtained. The result is the generalization of Bojdecki's model, where before and after the change independent processes are observed.

Keywords:

• disorder problem
• sequential detection
• optimal stopping
• Markov process
• change point

AMS Subject Classification::

• 60G40
• 60K99
• 90D60

Acknowledgements

The authors gratefully acknowledge the helpful suggestions of the anonymous referees and the editor during the preparation of this paper.