In this note we settle a question posed by Kasahara, Maejima, and Vervaat. We show that the [alpha]-stable Lévy motion is the only (1/[alpha])-self-similar [alpha]-stable process with stationary increments if 0 [alpha] 1. We also introduce new classes of (1/[alpha])-self-similar...

Let [mu] be a [sigma]-finite measure, R = (rij) be a covariance matrix, and B1,..., Bn be dependent Gaussian measures satisfying EBi(A1) Bj(A2) = rij[mu](A1 [down curve] A2). Multiple integrals of the form In(f) = [integral operator]f(x1,..., xn) dB1(x1) ... dBn(xn), with f [set membership,...

This paper studies the sample path properties of stochastic processes represented by multiple symmetric [alpha]-stable integrals. It relates the "smoothness" of the sample paths to the "smoothness" of the (non-random) integrand. It also contains results about the behavior of the distribution of...

C. D. Hardin, Jr., G. Samorodnitsky, and M. S. Taqqu (1991,Ann. Appl. Probab. 1 582-612) have shown that the regression E[Y X = x] is typically asymptotically linear when (X, Y) is an [alpha]-stable random vector with [alpha] 2. We provide necessary and sufficient conditions for asymptotic...