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By a well known result of Philipp (1975), the discrepancy D N (ω) of the sequence (n k ω) k≥1 mod 1 satisfies the law of the iterated logarithm under the Hadamard gap condition n k+1 /n k ≥ q > 1 (k = 1, 2,. . .). Recently Berkes, Philipp and Tichy (2006) showed that this result remains valid, under Diophantine conditions on (n k), for subexpenen-tially(More)
We study the almost sure convergence of the Bartlett estimator for the asymp-totic variance of the sample mean of a stationary weekly dependent process. We also study the a. s. behavior of this estimator in the case of long-range dependent observations. In the weakly dependent case, we establish conditions under which the estimator is strongly consistent.(More)
We prove a law of the iterated logarithm for the Kolmogorov-Smirnov statistic, or equivalently, the discrepancy of sequences (n k ω) mod 1. Here (n k) is a sequence of integers satisfying a sub-Hadamard growth condition and such that linear Diophantine equations in the variables n k do not have too many solutions. The proof depends on a martingale embedding(More)
Improvement of ankle proprioception through physiotherapy (a.k.a. proprioceptive training) is a widely accepted conservative treatment modality of chronic functional lateral ankle instability. Clinical studies provided controversial data on its proprioceptive effect. Aim of this study was to gain evidence on the efficacy of proprioceptive training on ankle(More)
We have tested the hypothesis that training with moderate- (MT), strenuous- (ST), or over- (OT) load can cause alterations in memory, lipid peroxidation, protein oxidation, DNA damage, activity of 8-oxoG-DNA glycosylase (OGG1) and brain-derived neurotrophic factor (BDNF), in rat brain. Rat memory was assessed by a passive avoidance test and the ST and OT(More)
Chronic swimming training and phytotherapeutic supplementation are assumed to alleviate oxidative damage, and support cell survival in the brain. The effect of forced, chronic swimming training, and enriched lab chow containing 1% (w/w) dried nettle (Urtica dioica) leaf were investigated for oxidative stress, inflammation and neurotrophic markers in Wistar(More)
We introduce new entropy concepts measuring the size of a given class of increasing sequences of positive integers. Under the assumption that the entropy function of A is not too large, many strong limit theorems will continue to hold uniformly over all sequences in A. We demonstrate this fact by extending the Chung-Smirnov law of the iterated logarithm on(More)
We investigate the estimation of parameters in the random coefficient autoregressive model X k = (ϕ + b k)X k−1 + e k , where (ϕ, ω 2 , σ 2) is the parameter of the process, Eb 2 0 = ω 2 , Ee 2 0 = σ 2. We consider a nonstationary RCA process satisfying E log |ϕ + b 0 | ≥ 0 and show that σ 2 cannot be estimated by the quasi-maximum likelihood method. The(More)