A universal result in almost sure central limit theorem for products of sums of partial sums under mixing sequence

作者：Zhang, Yong^*

来源：Stochastics-An International Journal of Probability and Stochastic Reports, 2016, 88(6): 803-812.

DOI：10.1080/17442508.2016.1146281

• Almost sure central limit theorem
• products of sums of partial sums
• phi-mixing sequence
• logarithmic averages

Let {Xn, n >= 1} be a strictly stationary f-mixing sequence of positive random variables with EX1 = mu > 0, and VarX1 = s2 < 8. Denote Sn = mu ni = 1 Xi, Tn = mu ni = 1 Si and. = s/ mu the coefficient of variation. Under some suitable conditions, the author shows that a universal version of almost sure central limit theorem for products of sums of partial sums holds under the assumptions that the mixing coefficients satisfy mu 8 n= 1 f1/ 2( n) < 8, moreover we no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences.

• 出版日期2016
• 单位吉林大学