For product probability measures \mu^n, we obtain necessary and sufficient conditions (in terms of \mu) for dimension free isoperimetric inequalities of the form \mu^n (A + h[-1,1]^n)\ge R_h(\mu^n(A)) to hold; for a ...

A dimension free lower bound is found for isoperimetric constants of product probability measures. From this, some analytic inequalities are derived.

If the half-spaces of the form {x\in R^n: x_1 \le c} are extremal in the isoperimetric problem for the product measure \mu^n, n\ge 2, then \mu is Gaussian.

Converse Poincaré type inequalities are obtained within the class of smooth convex functions. This is, in particular, applied to the double exponential distribution.

This work is concerned with the prediction problem for a class of L^p-random fields. For this class of fields, we derive prediction error formulas, spectral factorizations, and orthogonal decompositions.

Nonparametric methods for the estimation of the Levy density of a Levy process X are developed. Estimators that can be written in terms of the "jumps" of X are introduced, and so are discrete-data based approximations. A ...

The maximal variance of Lipschitz functions (with respect to the \ell_1-distance) of independent random vectors is found. This is then used to solve the isoperimetric problem, uniformly in the class of product probability ...

It is shown here how to extend the spectral characterization of the strong law of large numbers for weakly stationary processes to certain singular averages. For instance, letting {X_t, t \in R^3}, be a weakly stationary ...

The optimal constants in the multiplicative Sobolev inequalities where the gradient is estimated in the L_1-norm and the function in two different Lebesgue norms are found. With the optimal constants, these inequalities ...