Nous considérons un cadre non conventionnel de moyenne de la forme , où , est un processus stochastique ou un système dynamique suffisamment mélangeant tandis que , et , ont une croissance sur-linéaire. Nous montrons que le terme d’erreur après renormalisation est asymptotiquement gaussien.
We consider “nonconventional” averaging setup in the form , where , is either a stochastic process or a dynamical system with sufficiently fast mixing while , and , grow faster than linearly. We show that the properly normalized error term in the “nonconventional” averaging principle is asymptotically Gaussian.
Mots clés : averaging, limit theorems, martingales, hyperbolic dynamical systems
@article{AIHPB_2014__50_1_236_0, author = {Kifer, Yuri}, title = {Nonconventional limit theorems in averaging}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {236--255}, publisher = {Gauthier-Villars}, volume = {50}, number = {1}, year = {2014}, doi = {10.1214/12-AIHP514}, mrnumber = {3161530}, language = {en}, url = {http://www.numdam.org/articles/10.1214/12-AIHP514/} }
TY - JOUR AU - Kifer, Yuri TI - Nonconventional limit theorems in averaging JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2014 SP - 236 EP - 255 VL - 50 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/12-AIHP514/ DO - 10.1214/12-AIHP514 LA - en ID - AIHPB_2014__50_1_236_0 ER -
Kifer, Yuri. Nonconventional limit theorems in averaging. Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 1, pp. 236-255. doi : 10.1214/12-AIHP514. http://www.numdam.org/articles/10.1214/12-AIHP514/
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