The Wiener disorder problem seeks to determine a stopping time which is as close as possible to the (unknown) time of 'disorder' when the drift of an observed Wiener process changes from one value to another. In this paper we present a solution of the Wiener disorder problem when the horizon is...

If B = (Bt)t [greater-or-equal, slanted] 0 is a standard Brownian motion started at x under Px for x [greater-or-equal, slanted] 0, and [tau] is any stopping time for B with Ex([tau]) < [infinity], then for each p > 1 the following inequality is shown to be sharp: The sharpness is realized through the stopping times of the...</[infinity],>