On sequentially detecting an abrupt change in a stochastic process

Well-known procedures exist for sequentially detecting abrupt changes in the distribution of a stochastic process with independent and identically distributed (IID) samples. An analysis is made of the asymptotic optimality of a class of such procedures by comparing expected delay as the false alarm rate is sufficiently small. The criterion used as minimum expected delay, while previously the procedures were found to be optimal in the sense of minimizing only an upper bound of the expected delay. It is proved that Page´s (1954) repeated sequential probability ratio test (SPRT) procedure is asymptotically optimal in view of this more practically useful criterion