关于自正则化的Erds-Rényi-Shepp型强大数律的收敛速度

On the convergence rates of self-regularization Erds-Rényi-Shepp type strong law of large numbers.

利用适当的自正则化因子 ,Csorg o″ M.等建立了 Erdos- Rényi- Shepp型强大数律 .本文考察了其结果的收敛速度 ,获得其收敛速度为 O( k-1n log kn) ,其中 kn=[c log n]( c>0 )

Using the suitable self regularization for partial sum of i.i.d. random variables, Csrg o ″ et al established the Erds Rényi Shepp type strong law of large numbers. The aim of this paper is to generalize and extend their results. It shows that the exact convergence rates of the limit can be O(k -1 nlog k n) ,where k n=[c log n](c>0).