-norm of infinitely divisible random vectors and certain stochastic integrals.
-Khintchine-Bonami inequality in free probability
We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length (). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.
inequalities for functionals of brownian motion
La convergence de la série de Picard pour les EDS
Laplace transform estimates and deviation inequalities
Les inégalités de Khintchine-Kahane, d'après C. Borell
L'Hospital type results for monotonicity, with applications.
L'Hospital type rules for monotonicity: Applications to probability inequalities for sums of bounded random variables.
L'Hospital type rules for oscillation, with applications.
Lipschitzian norm estimate of one-dimensional Poisson equations and applications
By direct calculus we identify explicitly the lipschitzian norm of the solution of the Poisson equation in terms of various norms of g, where is a Sturm–Liouville operator or generator of a non-singular diffusion in an interval. This allows us to obtain the best constant in the L1-Poincaré inequality (a little stronger than the Cheeger isoperimetric inequality) and some sharp transportation–information inequalities and concentration inequalities for empirical means. We conclude with several illustrative...
Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses
Logarithmic Sobolev inequality for zero-range dynamics: independence of the number of particles.