Tauberian theorems for summability transforms.
Techniques probabilistes pour l'étude de problèmes d'isomorphismes entre espaces de Banach
Teoría ergódica y simetrización.
We study the relations between simetrization by a limiting process of probabilities and functions defined on a metric compacy product space and their ergodic properties.
The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences
Suppose that X1, X2, … is some stationary zero mean Gaussian sequence with unit variance. Let {kn} be a certain nondecreasing sequence of positive integers, [...] denote the kn largest maximum of X1, … Xn. We aim at proving the almost sure central limit theorems for the suitably normalized sequence [...] under certain additional assumptions on {kn} and the covariance function [...]
The almost sure invariance principle for the empirical process of U-statistic structure
The bundle convergence in von Neumann algebras and their -spaces
A stronger version of almost uniform convergence in von Neumann algebras is introduced. This "bundle convergence" is additive and the limit is unique. Some extensions of classical limit theorems are obtained.
The distribution of unbounded random sets and the multivalued strong law of large numbers in nonreflexive Banach spaces.
The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces
We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.
The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile
The ergodic theory of positive operators on continuous functions
The fractional mixed fractional brownian motion and fractional brownian sheet
We introduce the fractional mixed fractional Brownian motion and fractional Brownian sheet, and investigate the small ball behavior of its sup-norm statistic. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test. Finally, when we consider the sup-norm statistic, the necessity part is given by a second integral test.
The functional moderate deviations for Harris recurrent Markov chains and applications
The law of large numbers for -statistics under absolute regularity.
The law of the iterated logarithm for a triangular array of empirical processes.
The law of the iterated logarithm for exchangeable random variables.
The law of the iterated logarithm for the multivariate kernel mode estimator
Let be the mode of a probability density and its kernel estimator. In the case is nondegenerate, we first specify the weak convergence rate of the multivariate kernel mode estimator by stating the central limit theorem for . Then, we obtain a multivariate law of the iterated logarithm for the kernel mode estimator by proving that, with probability one, the limit set of the sequence suitably normalized is an ellipsoid. We also give a law of the iterated logarithm for the norms, , of ....
The law of the iterated logarithm for the multivariate kernel mode estimator
Let θ be the mode of a probability density and θn its kernel estimator. In the case θ is nondegenerate, we first specify the weak convergence rate of the multivariate kernel mode estimator by stating the central limit theorem for θn - θ. Then, we obtain a multivariate law of the iterated logarithm for the kernel mode estimator by proving that, with probability one, the limit set of the sequence θn - θ suitably normalized is an ellipsoid. We also give a law of the iterated logarithm for the...
The laws of Chung and Hirsch for Cauchy's principal values related to Brownian local times.
The "local" law of the iterated logarithm for processes related to Lévy's stochastic area process
The principle of large deviations for martingale additive functionals of recurrent Markov processes.