Nonconventional limit theorems in averaging
Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 1, pp. 236-255.

Nous considérons un cadre non conventionnel de moyenne de la forme dX ε (t) dt=εB(X ε (t), 𝛯(q 1 (t)),𝛯(q 2 (t)),...,𝛯(q (t)))𝛯(t), t0 est un processus stochastique ou un système dynamique suffisamment mélangeant tandis que q j (t)=α j t, α 1 <α 2 <<α k et q j , j=k+1,..., 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 dX ε (t) dt=εB(X ε (t), 𝛯(q 1 (t)),𝛯(q 2 (t)),...,𝛯(q (t))) where 𝛯(t), t0 is either a stochastic process or a dynamical system with sufficiently fast mixing while q j (t)=α j t, α 1 <α 2 <<α k and q j , j=k+1,..., grow faster than linearly. We show that the properly normalized error term in the “nonconventional” averaging principle is asymptotically Gaussian.

DOI : https://doi.org/10.1214/12-AIHP514
Classification : 34C29,  60F17,  37D20
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 = {www.numdam.org/item/AIHPB_2014__50_1_236_0/}
}
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/item/AIHPB_2014__50_1_236_0/

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