Über starke Konvergenz in der Theorie der c-Gleichverteilung.
Un principe de sous-suites dans la théorie des probabilités
Un théorème de Banach et Saks et un principe de sous-suites dans la théorie des probabilités
Un théorème ergodique polynômial ponctuel pour les endomorphismes exacts et les K-systèmes
Une loi des grands nombres pour des systèmes de diffusions avec interaction et à coefficients non bornés
Une loi du logarithme itéré pour les martingales locales multidimensionnelles et son application en régression linéaire stochastique
Uniform deterministic equivalent of additive functionals and non-parametric drift estimation for one-dimensional recurrent diffusions
Usually the problem of drift estimation for a diffusion process is considered under the hypothesis of ergodicity. It is less often considered under the hypothesis of null-recurrence, simply because there are fewer limit theorems and existing ones do not apply to the whole null-recurrent class. The aim of this paper is to provide some limit theorems for additive functionals and martingales of a general (ergodic or null) recurrent diffusion which would allow us to have a somewhat unified approach...
Uniform law of large numbers
Universally typical sets for ergodic sources of multidimensional data
We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to construct sequences of multidimensional array sets which in the limit build the generated samples of any ergodic source of entropy rate below an with...