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],>

Let (Xt)t[greater-or-equal, slanted]0 be a non-singular (not necessarily recurrent) diffusion on starting at zero, and let [nu] be a probability measure on Necessary and sufficient conditions are established for [nu] to admit the existence of a stopping time [tau]* of (Xt) solving the Skorokhod...