Nonconventional moderate deviations theorems and exponential concentration inequalities

2018/05/02 by Yeor Hafouta, Hafouta, Yeor
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1805.00849

24 pages; In the third version Young towers can be considered in Theorems 2.3 and 2.4. In the fourth, a corrected proof of Theorem 6.3 appears. To appear in AIHP

openalex publication_date 2018/05/02 · arxiv created 2019/02/08 · arxiv updated 2019/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain moderate deviations theorems and exponential (Bernstein type) concentration inequalities for "nonconventional" sums of the form S_N=∑_n=1^N (F(ξ_q1(n),ξ_q2(n),...,ξ_{q_ℓ(n)})- F).

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