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,
设{X,Xn,n≥1}是独立同分布正态随机变量序列,EX=0且EX2=σ2>0,Sn=sum (Xk) form k=1 to n,λ(ε) =sum form (P(|Sn|≥ nε)) form n=1 to ∞.在本文中,我们证明了存在正常数C1和C2,使得对足够小的ε>0,成立下列不等式C1ε3 ≤ε...设{X,Xn,n≥1}是独立同分布正态随机变量序列,EX=0且EX2=σ2>0,Sn=sum (Xk) form k=1 to n,λ(ε) =sum form (P(|Sn|≥ nε)) form n=1 to ∞.在本文中,我们证明了存在正常数C1和C2,使得对足够小的ε>0,成立下列不等式C1ε3 ≤ε2λ(ε)-σ2+ε2 /2 ≤ C2ε3.展开更多
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,
文摘设{X,Xn,n≥1}是独立同分布正态随机变量序列,EX=0且EX2=σ2>0,Sn=sum (Xk) form k=1 to n,λ(ε) =sum form (P(|Sn|≥ nε)) form n=1 to ∞.在本文中,我们证明了存在正常数C1和C2,使得对足够小的ε>0,成立下列不等式C1ε3 ≤ε2λ(ε)-σ2+ε2 /2 ≤ C2ε3.
