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Une étude asymptotique probabiliste des coefficients d’une série entière

Bernard Candelpergher, Michel Miniconi (2014)

Journal de Théorie des Nombres de Bordeaux

En partant des idées de Rosenbloom [7] et Hayman [5], Luis Báez-Duarte donne dans [1] une preuve probabiliste de la formule asymptotique de Hardy-Ramanujan pour les partitions d’un entier. Le principe général de la méthode repose sur la convergence en loi d’une famille de variables aléatoires vers la loi normale. Dans notre travail nous démontrons un théorème de type Liapounov (Chung [2]) qui justifie cette convergence. L’obtention de formules asymptotiques simples nécessite une condition dite Gaussienne...

Uniform asymptotic normality for the Bernoulli scheme

Wojciech Niemiro, Ryszard Zieliński (2007)

Applicationes Mathematicae

It is easy to notice that no sequence of estimators of the probability of success θ in a Bernoulli scheme can converge (when standardized) to N(0,1) uniformly in θ ∈ ]0,1[. We show that the uniform asymptotic normality can be achieved if we allow the sample size, that is, the number of Bernoulli trials, to be chosen sequentially.

Uniform deterministic equivalent of additive functionals and non-parametric drift estimation for one-dimensional recurrent diffusions

D. Loukianova, O. Loukianov (2008)

Annales de l'I.H.P. Probabilités et statistiques

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...

Universality for random tensors

Razvan Gurau (2014)

Annales de l'I.H.P. Probabilités et statistiques

We prove two universality results for random tensors of arbitrary rank D . We first prove that a random tensor whose entries are N D independent, identically distributed, complex random variables converges in distribution in the large N limit to the same limit as the distributional limit of a Gaussian tensor model. This generalizes the universality of random matrices to random tensors. We then prove a second, stronger, universality result. Under the weaker assumption that the joint probability distribution...

Universally typical sets for ergodic sources of multidimensional data

Tyll Krüger, Guido F. Montúfar, Ruedi Seiler, Rainer Siegmund-Schultze (2013)

Kybernetika

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 h 0 with...

Currently displaying 21 – 40 of 45