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134 Bercu, B. , On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications, Stochastic Process. Appl. 111 (2004

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. , Almost sure central limit theorems for strongly mixing and associated random variables , Inter. J. of Math. , 29 ( 3 ) ( 2001 ), 125 – 131 . [5] L ehmann , E. L

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Abstract  

By applying the Skorohod martingale embedding method, a strong approximation theorem for partial sums of asymptotically negatively dependent (AND) Gaussian sequences, under polynomial decay rates, is established. As applications, the law of the iterated logarithm, the Chung-type law of the iterated logarithm and the almost sure central limit theorem for AND Gaussian sequences are derived.

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187 196 IBRAGIMOV, I. and LIFSHITS, M., On the convergence of generalized moments in almost sure central limit theorem, Statist. Probab. Lett. 40 (1998), 343-351. MR 99m

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almost sure central limit theorem under minimal conditions, Stat Probab. Letters , 37 (1998), 67–76. Horváth L. An almost sure central limit theorem under minimal conditions

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theorem and domains of attraction, Probab. Theory Related Fields 102 (1995), 1-17. MR 96j :60033 On the almost sure central limit theorem and domains of attraction Probab. Theory Related Fields

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BERKES, I., On the almost sure central limit theorem and domains of attraction, Probab. Theory Related Fields 102 (1995), 1-17. MR 96j :60033 On the almost sure central limit theorem and domains of attraction

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LetS n be the partial sums of ?-mixing stationary random variables and letf(x) be a real function. In this note we give sufficient conditions under which the logarithmic average off(S n/sn) converges almost surely to ?-8 8 f(x)dF(x). We also obtain strong approximation forH(n)=?k=1 n k -1 f(S k/sk)=logn ?-8 8 f(x)dF(x) which will imply the asymptotic normality ofH(n)/log1/2 n. But for partial sums of i.i.d. random variables our results will be proved under weaker moment condition than assumed for ?-mixing random variables.

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-Sklodowska, Lublin LVI 1 18 Fazekas, I. and Rychlik, Z., Almost sure central limit theorems for random fields, Math

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