TY - JOUR
T1 - Strong approximations for nonconventional sums and almost sure limit theorems
AU - Kifer, Yuri
PY - 2013
Y1 - 2013
N2 - Abstract We improve, first, a strong invariance principle from Kifer (2013) [10] for nonconventional sums of the form ∑n=1[Nt]F(X(n),X(2n),.,X(ℓn)) (normalized by 1/N) where X(n),n≥0's is a sufficiently fast mixing vector process with some moment conditions and stationarity properties and F satisfies some regularity conditions. Applying this result we obtain next a version of the law of iterated logarithm for such sums, as well as an almost sure central limit theorem. Among motivations for such results are their applications to multiple recurrence for stochastic processes and dynamical systems.
AB - Abstract We improve, first, a strong invariance principle from Kifer (2013) [10] for nonconventional sums of the form ∑n=1[Nt]F(X(n),X(2n),.,X(ℓn)) (normalized by 1/N) where X(n),n≥0's is a sufficiently fast mixing vector process with some moment conditions and stationarity properties and F satisfies some regularity conditions. Applying this result we obtain next a version of the law of iterated logarithm for such sums, as well as an almost sure central limit theorem. Among motivations for such results are their applications to multiple recurrence for stochastic processes and dynamical systems.
KW - Almost sure central limit theorem
KW - Dynamical systems
KW - Martingale approximation
KW - Mixing
KW - Strong approximations
UR - http://www.scopus.com/inward/record.url?scp=84875148516&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2013.02.009
DO - 10.1016/j.spa.2013.02.009
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AN - SCOPUS:84875148516
SN - 0304-4149
VL - 123
SP - 2286
EP - 2302
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 6
ER -