Correction to “Domains of attraction in several dimensions”
Correction : « Vitesse de convergence en loi pour des solutions d'équations différentielles stochastiques vers une diffusion »
Die Geschwindigkeit der Glivenko-Cantelli-Konvergenz gemessen in der Prohorov-Metrik.
Diskrepanz in separablen metrischen Räumen.
Domains of partial attraction in several dimensions
EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires
Empirical estimates in stochastic optimization via distribution tails
“Classical” optimization problems depending on a probability measure belong mostly to nonlinear deterministic optimization problems that are, from the numerical point of view, relatively complicated. On the other hand, these problems fulfil very often assumptions giving a possibility to replace the “underlying” probability measure by an empirical one to obtain “good” empirical estimates of the optimal value and the optimal solution. Convergence rate of these estimates have been studied mostly for...
Ergodicity of a certain class of non Feller models : applications to and Markov switching models
We provide an extension of topological methods applied to a certain class of Non Feller Models which we call Quasi-Feller. We give conditions to ensure the existence of a stationary distribution. Finally, we strengthen the conditions to obtain a positive Harris recurrence, which in turn implies the existence of a strong law of large numbers.
Ergodicity of a certain class of Non Feller Models: Applications to ARCH and Markov switching models
We provide an extension of topological methods applied to a certain class of Non Feller Models which we call Quasi-Feller. We give conditions to ensure the existence of a stationary distribution. Finally, we strengthen the conditions to obtain a positive Harris recurrence, which in turn implies the existence of a strong law of large numbers.
Erneuerungsprozesse.
Espaces -lisses et -convexes. Inégalités de Burkholder
Espaces -lisses. Réarrangements
Estimates of Hellinger integrals of infinitely divisible distributions
Euclidean distances on signed measures and application to Berry-Esséen theorems. (Distances euclidiennes sur les mesures signées et application à des théorèmes de Berry-Esséen.)
Examples of convergence and non-convergence of Markov chains conditioned not to die.
Finitely-additive, countably-additive and internal probability measures
We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an internal probability measure and its push-down measure is infinitesimal. As an application to standard probability theory, we show that every finitely-additive Borel probability measure on a separable metric space is a limit of a sequence of countably-additive Borel probability measures in the sense that for all bounded...
Gaussian concentration in the Kantorovich metric of distributions of random variables and the quantile functions.
Invariance principles for random walks conditioned to stay positive
Let {Snbe a random walk in the domain of attraction of a stable law , i.e. there exists a sequence of positive real numbers ( an) such that Sn/anconverges in law to . Our main result is that the rescaled process (S⌊nt⌋/an, t≥0), when conditioned to stay positive, converges in law (in the functional sense) towards the corresponding stable Lévy process conditioned to stay positive. Under some additional assumptions, we also prove a related invariance principle for the random walk killed at its first...
Invariance principles in Hölder spaces.
Iterates of a convolution on a non abelian group