We study the convergence of the ergodic averages where is a bounded sequence and a strictly increasing sequence of integers such that for some . Moreover we give explicit such sequences and and we investigate in particular the case where is a -multiplicative sequence.
Nous étudions la convergence de moyennes ergodiques où est une suite bornée et une suite d’entiers strictement croissante tels que avec . De plus nous donnons des exemples explicites de telles suites et puis, nous nous intéressons aux cas où est une suite - multiplicative.
Keywords: weighted ergodic averages, central limit theorem, almost sure convergence, $q$-multiplicative sequences, substitutive sequences, generalized Thue-Morse sequences
Mot clés : moyennes ergodiques pondérées, théorème ..., convergence presque sûre, suites multiplicatives $q$, suites substitutives, suite de Thue-Morse généralisées
@article{AIF_2002__52_2_561_0, author = {Durand, Fabien and Schneider, Dominique}, title = {Ergodic averages with deterministic weights}, journal = {Annales de l'Institut Fourier}, pages = {561--583}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {52}, number = {2}, year = {2002}, doi = {10.5802/aif.1894}, mrnumber = {1906483}, zbl = {1054.37003}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1894/} }
TY - JOUR AU - Durand, Fabien AU - Schneider, Dominique TI - Ergodic averages with deterministic weights JO - Annales de l'Institut Fourier PY - 2002 SP - 561 EP - 583 VL - 52 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1894/ DO - 10.5802/aif.1894 LA - en ID - AIF_2002__52_2_561_0 ER -
%0 Journal Article %A Durand, Fabien %A Schneider, Dominique %T Ergodic averages with deterministic weights %J Annales de l'Institut Fourier %D 2002 %P 561-583 %V 52 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1894/ %R 10.5802/aif.1894 %G en %F AIF_2002__52_2_561_0
Durand, Fabien; Schneider, Dominique. Ergodic averages with deterministic weights. Annales de l'Institut Fourier, Volume 52 (2002) no. 2, pp. 561-583. doi : 10.5802/aif.1894. http://archive.numdam.org/articles/10.5802/aif.1894/
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