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强不变原理中的最佳速度
张
Science in China Series A-Mathematics Physics Astronomy & Technological Science (in Chinese)1 Jan 1995Open access
Journal articleOpen access
强不变原理中的最佳速度
张 · Science in China Series A-Mathematics Physics Astronomy & Technological Science (in Chinese) · 1995
Abstract
设{X n }为i.i.d.r.v.s.,EX 1 =0,EX 1 ~2=1,S_n=sum from i=1 to n(X i ),H(x)>0 (x≥0)为非降连续函数,对某γ>0和x 0 >0,当x≥x 0 时,x -2-γ H(x)非降,x -1 logH(x)非增,且x -1 logH(x)→0(x→∞),则有一标准Wiener过程{W(t),t≥0},使得 S n -W(n)=O(invH(n))a.s.(n→∞)的充分必要条件是:对任何t>0有EH(t|X 1 |)<∞.