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...

Several inequalities of Kahane-Khintchine's type in certain Orlicz spaces are proved. For this, the classical symmetrization technique is used and four basically different methods have been presented. The first two are based on the well-known estimates for subnormal random variables, the third...

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],>