8.4.4 A Brownian motion X.t/ either (1) has drift  D C1 2  > 0, or (2) has drift

 D ????1 2  < 0, and it is desired to determine which is the case by observing the process for a fixed duration  . If X. / > 0, then the decision will be that  D C12

; If X. /  0, then  D ????12

 will be stated. What should be the length  of the observation period if the design error probabilities are set at D D 0:05? Use  D 1 and  D 2. Compare this fixed duration with the average duration of the sequential decision plan in the example of Section 8.4.1.