Let (Xt)t[set membership, variant]R[phi] be a diffusion on which starts in x and assume that a stationary initial distribution exists with continouos density [pi]. Then where T(x-[var epsilon], x + [epsilon]) denotes the first exit time of (x - [var epsilon], x + [epsilon]) and Zx[epsilon]) is...

Let [mu]1+ and [mu]2+ be the distributions of the first ascending ladder heights of random walks with step distributions [mu]1 and [mu]2, respectively. We obtain an estimate for the distance of [mu]1+ and [mu]2+ in terms of the characteristic functions of [mu]1 and [mu]2.