TY - JOUR
T1 - Nonconventional limit theorems in averaging
AU - Kifer, Yuri
PY - 2014/2
Y1 - 2014/2
N2 - We consider "nonconventional" averaging setup in the form {equation presented} where (t), t ≥ 0 is either a stochastic process or a dynamical system with sufficiently fast mixing while qj (t) = αjt, α1 < α2 < . . . < αk and qj, j = k + 1, . . . , l grow faster than linearly. We show that the properly normalized error term in the "nonconventional" averaging principle is asymptotically Gaussian.
AB - We consider "nonconventional" averaging setup in the form {equation presented} where (t), t ≥ 0 is either a stochastic process or a dynamical system with sufficiently fast mixing while qj (t) = αjt, α1 < α2 < . . . < αk and qj, j = k + 1, . . . , l grow faster than linearly. We show that the properly normalized error term in the "nonconventional" averaging principle is asymptotically Gaussian.
KW - Averaging
KW - Hyperbolic dynamical systems
KW - Limit theorems
KW - Martingales
UR - http://www.scopus.com/inward/record.url?scp=84891926929&partnerID=8YFLogxK
U2 - 10.1214/12-AIHP514
DO - 10.1214/12-AIHP514
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84891926929
SN - 0246-0203
VL - 50
SP - 236
EP - 255
JO - Annales de l'institut Henri Poincare (B) Probability and Statistics
JF - Annales de l'institut Henri Poincare (B) Probability and Statistics
IS - 1
ER -