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A roumula for the density of the norm of stable random vectors in Hilbert spaces
Complements on decoupling inequalities for multilinear functions in stable random vectors
For a symmetric a-stable random vector (XI.,. . , X,,X ,+ ,) with 1 < a < 2 and spectral measure r, we find a necessary and sufficient condition in terms of r for the conditional variance Var(X,+l ...
Let (5,J be a sequence of random vectors with values in a Banach space X with distributions pen weakly converging to a given distribution p. We characterize a general form of a distribution of a we...
An SorS random vector X is pserbstable, or < fl d 2, if X: YeiM for some symmetric /?-stable random vector Y, 8 3 0 a random variable with the Laplace transform exp {-@), Y and B are independent. W...
The sums of i.i.d. random vectors with compactly supported and absolutely continuous distribution are considered. Under some conditions the strong form of the local limit theorem for large deviatio...
It is shown that the tail probabilities of a strictly (r, a)-semistable (0 < r < 1,0 < n < 2, a # 1) Banach space valued random vector X and its symmetrized counterpart are "uniformly" comparable i...
A class of multidimensiond distributions is considered. This class contains all the elliptically contoured distributions having sup-exponential weight function. Each representative of the class dete...
We present an integral test to determine the limiting behavior of weighted sums of i.i.d. Rd-valued random vectors belonging to the (generalized) domain of operator semistable attraction of some no...
A random vector X is B-substable, BE(O, 21, Z there exist a symmetric 8-stable random vector Y and a random variable 8 3 0 independent of l' such that X Y @'I8. In this paper we investigate strictl...
Equivalent upper and lower bounds for the L1 norm of Hilbert space valued infinitely divisible random variables are obtained and used to find bounds for different types of stochastic integrals.
In this article, we derive a new generalization of Chebyshev inequality for random vectors. We demonstrate that the new generalization is much less conservative than the classical generalization.

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