A Berry-Esseen theorem on semisimple Lie groups
A Bound on the Expected Overshoot for some Concave Boundaries.
A bound on the moment generating function of a sum of dependent variables with an application to simple random sampling without replacement
A free analogue of the transportation cost inequality on the circle
A Gaussian correlation inequality and its applications to small ball probabilities.
A generalized Kahane-Khinchin inequality
The inequality with an absolute constant C, and similar ones, are extended to the case of belonging to an arbitrary normed space X and an arbitrary compact group of unitary operators on X instead of the operators of multiplication by .
A generalized Ostrowski type inequality for a random variable whose probability density function belongs to .
A generalized residual information measure and its properties.
A geometric approach to correlation inequalities in the plane
By elementary geometric arguments, correlation inequalities for radially symmetric probability measures are proved in the plane. Precisely, it is shown that the correlation ratio for pairs of width-decreasing sets is minimized within the class of infinite strips. Since open convex sets which are symmetric with respect to the origin turn out to be width-decreasing sets, Pitt’s Gaussian correlation inequality (the two-dimensional case of the long-standing Gaussian correlation conjecture) is derived...
A Hájek-Rényi-type maximal inequality and strong laws of large numbers for multidimensional arrays.
A log-Sobolev type inequality for free entropy of two projections
We prove a kind of logarithmic Sobolev inequality claiming that the mutual free Fisher information dominates the microstate free entropy adapted to projections in the case of two projections.
A maximal inequality for martingale local times
A Measure Concentration Inequality for Contracting Markov Chains.
A multivariate version of Hoeffding's inequality.
A natural derivative on [0, n] and a binomial Poincaré inequality
We consider probability measures supported on a finite discrete interval [0, n]. We introduce a new finite difference operator ∇n, defined as a linear combination of left and right finite differences. We show that this operator ∇n plays a key role in a new Poincaré (spectral gap) inequality with respect to binomial weights, with the orthogonal Krawtchouk polynomials acting as eigenfunctions of the relevant operator. We briefly discuss the relationship of this operator to the problem of optimal transport...
A new proof of Kellerer’s theorem
In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
A new proof of Kellerer’s theorem
In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
A note on a weighted Ostrowski type inequality for cumulative distribution functions.
A note on an individual bioequivalence setting.
A note on maximal inequalities