Sur le théorème de Khintchine
Sur l'équation de Poisson
Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi
Sur les mesures invariantes de certaines chaînes de Markov définies par des transformations homographiques
Sur les temps de coupure des marches aléatoires réfléchies
Sur une classe des fonctionnelles des processus stables et des marches aléatoires
Survival probabilities of autoregressive processes
Given an autoregressive process X of order p (i.e. Xn = a1Xn−1 + ··· + apXn−p + Yn where the random variables Y1, Y2,... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time N (survival or persistence probability). Depending on the coefficients a1,..., ap and the distribution of Y1, we state conditions under which the survival probability decays polynomially, faster than polynomially or converges to a positive constant....
Survival probability approach to the relaxation of a macroscopic system in the defect-diffusion framework
The main objective of this paper is to present a new probabilistic model underlying the universal relaxation laws observed in many fields of science where we associate the survival probability of the system's state with the defect-diffusion framework. Our approach is based on the notion of the continuous-time random walk. To derive the properties of the survival probability of a system we explore the limit theorems concerning either the summation or the extremes: maxima and minima. The forms of...
Symmetric groups and expanders.
Tail and moment estimates for sums of independent random variables with logarithmically concave tails
For random variables , where is a sequence of symmetric, independent, identically distributed random variables such that is a concave function we give estimates from above and from below for the tail and moments of S. The estimates are exact up to a constant depending only on the distribution of ξ. They extend results of S. J. Montgomery-Smith [MS], M. Ledoux and M. Talagrand [LT, Chapter 4.1] and P. Hitczenko [H] for the Rademacher sequence.
Tail and moment estimates for sums of independent random vectors with logarithmically concave tails
Let be a sequence of independent symmetric real random variables with logarithmically concave tails. We consider a variable , where are vectors of some Banach space. We derive approximate formulas for the tail and moments of ∥X∥. The estimates are exact up to some universal constant and they extend results of S. J. Dilworth and S. J. Montgomery-Smith [1] for the Rademacher sequence and E. D. Gluskin and S. Kwapień [2] for real coefficients.
Tail behaviour of multiple random integrals and -statistics.
Tauberian theorems for summability transforms.
Tecniche per risolvere problemi di Testa e Croce
The best bounds in a theorem of Russell Lyons.
The Beurling estimate for a class of random walks.
The convolution equation of Choquet and Deny for probability measures on discrete semigroups
The critical case of the Cramer-Lundberg theorem on the asymptotic tail behavior of the maximum of a negative drift random walk.
The determination of the spectral multiplicity of a stochastic process by RKHS method
The distribution of non-commutative Rademacher series.