Strong approximations for nonconventional sums and almost sure limit theorems

Yuri Kifer

Stochastic Processes and their Applications, 2013, vol. 123, issue 6, 2286-2302

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.

Keywords: Strong approximations; Almost sure central limit theorem; Martingale approximation; Mixing; Dynamical systems (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:6:p:2286-2302

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DOI: 10.1016/j.spa.2013.02.009

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