Abstract: Time-sequential testing problems are studied in the counting process context. With a random time change of the counting process, it is shown that the associated optimal stopping time problem gets close to that for a Poisson process as sample size gets large. By making use of this observation, we propose a class of time-sequential tests, which is shown to be optimal in the sense that it has minimal asymptotic expected total time on-test with given bounds on error probabilities.
Key words and phrases: Asymptotic optimality, counting process, intensity process, likelihood ratio process, Poisson process, time-sequential test, time-sequential probability ratio test.