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.
The Rate of Convergence in the Functional Central Limit Theorem for Random Quadratic Forms with Some Applications to the Law of Iterated Logarithm.
The strong law of large numbers for dependent vector processes with decreasing correlation: “Double averaging concept”.
The strong law of large numbers for o-convergent random variables
The unconditional pointwise convergence of orthogonal seriesin over a von Neumann algebra
The paper is devoted to some problems concerning a convergence of pointwise type in the -space over a von Neumann algebra M with a faithful normal state Φ [3]. Here is the completion of M under the norm .
Théorèmes limites avec poids pour les martingales vectorielles
Théorèmes limites avec poids pour les martingales vectorielles
We give limit theorems specifying weak and strong rates of convergence associated to a quadratic extension of the martingale almost-sure central limit theorem. Some typical examples are discussed to illustrate how to make use of them in statistic.
Théorèmes limites pour les marches aléatoires sur le dual de
Théorèmes limites pour les temps locaux d'un processus stable symétrique
Theorems of Thron's type for random-valued vector functions and the Krein-Rutman theorem
We propose stochastic versions of some theorems of W. J. Thron [14] on the speed of convergence of iterates for random-valued functions on cones in Banach spaces.
Tightness of the Student -statistic.
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