A characterization of the domain of attraction of a normal distribution in a Hilbert space
A continuous mapping theorem for the argmin-set functional with applications to convex stochastic processes
For lower-semicontinuous and convex stochastic processes and nonnegative random variables we investigate the pertaining random sets of all -approximating minimizers of . It is shown that, if the finite dimensional distributions of the converge to some and if the converge in probability to some constant , then the converge in distribution to in the hyperspace of Vietoris. As a simple corollary we obtain an extension of several argmin-theorems in the literature. In particular, in...
A general bounded continuous moment problem and its sets of uniqueness
A limit theorem for functionals of a Poisson process
A metric property of some random functions
A *-mixing convergence theorem for convex set valued processes.
A New Isoperimetric Inequality for Product Measure and the Tails of Sums of Independent Variables.
A noncompact Choquet theorem
A non-Skorokhod topology on the Skorokhod space.
A note on a mean ergodic theorem
A note on almost sure convergence and convergence in measure
The present article studies the conditions under which the almost everywhere convergence and the convergence in measure coincide. An application in the statistical estimation theory is outlined as well.
A note on conservative measures on semigroups.
A note on Gauss measures which agree on small balls
A note on probabilistic representations of operator semigroups.
A representation of the characteristic functions of stable distributions in Hilbert spaces
A Simple Proof of the Majorizing Measure Theorem.
A theorem on weak type estimates for Riesz transforms and martingale transforms
The Riesz transforms of a positive singular measure satisfy the weak type inequalitywhere denotes Lebesgue measure and is a positive constant only depending on .
Admissible translates of stable measures
An inequality for the distribution of a sum of certain Banach space valued random variables
An isomorphic Dvoretzky's theorem for convex bodies
We prove that there exist constants C>0 and 0 < λ < 1 so that for all convex bodies K in with non-empty interior and all integers k so that 1 ≤ k ≤ λn/ln(n+1), there exists a k-dimensional affine subspace Y of satisfying . This formulation of Dvoretzky’s theorem for large dimensional sections is a generalization with a new proof of the result due to Milman and Schechtman for centrally symmetric convex bodies. A sharper estimate holds for the n-dimensional simplex.