Factorisation des distributions de Cantor
Factors and Roots of Large Measures on Connected Lie Groups.
Fernique type inequalities and moduli of continuity for l2-valued Ornstein-Uhlenbeck Processes
Finite dimensional determinants as characteristic functions of quadratic Wiener functionals.
FKG inequality for Brownian motion and stochastic differential equations.
FKN Theorem on the biased cube
We consider Boolean functions defined on the discrete cube equipped with a product probability measure , where and γ = √(α/β). This normalization ensures that the coordinate functions are orthonormal in . We prove that if the spectrum of a Boolean function is concentrated on the first two Fourier levels, then the function is close to a certain function of one variable. Our theorem strengthens the non-symmetric FKN Theorem due to Jendrej, Oleszkiewicz and Wojtaszczyk. Moreover, in the symmetric...
Fonctions de corrélation des fonctions pseudo-aléatoires
Fourier transform of the probability measures.
Fractional flux and non-normal diffusion.
Free and classical entropy over the circle.
Free generalized gamma convolutions.
From binomial expectations to the Black-Scholes formula: the main ideas
Functional inequalities for discrete gradients and application to the geometric distribution
We present several functional inequalities for finite difference gradients, such as a Cheeger inequality, Poincaré and (modified) logarithmic Sobolev inequalities, associated deviation estimates, and an exponential integrability property. In the particular case of the geometric distribution on we use an integration by parts formula to compute the optimal isoperimetric and Poincaré constants, and to obtain an improvement of our general logarithmic Sobolev inequality. By a...
Functional inequalities for discrete gradients and application to the geometric distribution
We present several functional inequalities for finite difference gradients, such as a Cheeger inequality, Poincaré and (modified) logarithmic Sobolev inequalities, associated deviation estimates, and an exponential integrability property. In the particular case of the geometric distribution on we use an integration by parts formula to compute the optimal isoperimetric and Poincaré constants, and to obtain an improvement of our general logarithmic Sobolev inequality. By a limiting procedure we...
Functional inequalities for heavy tailed distributions and application to isoperimetry.
Further development of an open problem.
Further results on the generalized cumulative entropy
Recently, a new concept of entropy called generalized cumulative entropy of order was introduced and studied in the literature. It is related to the lower record values of a sequence of independent and identically distributed random variables and with the concept of reversed relevation transform. In this paper, we provide some further results for the generalized cumulative entropy such as stochastic orders, bounds and characterization results. Moreover, some characterization results are derived...