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...

For a distribution [mu] on the unit interval we define the associated perpetuity [Psi]([mu]) as the distribution of 1+X1+X1X2+X1X2X3+..., where (Xn)n[set membership, variant] is a sequence of independent random variables with distribution [mu]. Such quantities arise in insurance mathematics and...

Given a statistical model for data which take values in Rd and have elliptically distributed errors, and affine equivariant estimators [mu] and [mu] of a mean vector in Rd[circle times operator]Rn and a d - d scatter matrix, expressions are given for the covarances of the estimators in terms of...

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.

Consider the standard model of renewal theory, where components with independent and identically distributed lifetimes are installed successively. We obtain the asymptotic distribution of the relative rank of the lifetime of the component in use at time t as t -- [infinity]. The result exhibits...