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

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.

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