Let X, X1, X2,… be i.i.d, random variables, and set Sn =X1+…+Xn,Mn=maxk≤n|Sk|,n≥1.Let an=o(√log n).By using the strong approximation, we prove that, if EX = 0,
基金supported by the National Natural Science Foundation of China(41888101,41830322)the Strategic Priority Research Program of Chinese Academy of Sciences(XDB26000000)+1 种基金the National Key Research&Development Program of China(2020YFC1521605)Youth Innovation Promotion Association of Chinese Academy of Sciences。
基金Supported by National Natural Science Foundation of China(Grant No.10771192)Natural Science Foundation of Zhejiang Province(Grant No.J20091364)
文摘Let X, X1, X2,… be i.i.d, random variables, and set Sn =X1+…+Xn,Mn=maxk≤n|Sk|,n≥1.Let an=o(√log n).By using the strong approximation, we prove that, if EX = 0,