SEQUENTIAL TESTING OF SIMPLE HYPOTHESES ABOUT COMPOUND POISSON PROCESSES

Abstract

Abstract. One of two simple hypotheses is correct about the unknown arrival rate and jump distribution of a compound Poisson process. We start observing the process, and the problem is to decide on the correct hypothesis as soon as possible and with the smallest probability of wrong decision. We find a Bayes-optimal sequential decision rule and describe completely how to calculate its parameters without any restrictions on the arrival rate and the jump distribution. 1