Limiting Behavior of Tail Series of Independent Random Variable

독립인 확률변수들의 Tail 합의 극한 성질에 대하여

  • Published : 2006.04.01

Abstract

For the almost co티am convergent series $S_n$ of independent random variables, by investigating the limiting behavior of the tail series, $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}X_i$, the rate of convergence of the series $S_n$ to a random variable S is studied in this paper. More specifically, the equivalence between the tail series weak law of large numbers and a limit law is established for a quasi-monotone decreasing sequence, thereby extending a result of Previous work to the wider class of the norming constants.

Keywords

Rate of Convergence;Series of Random Variables;Tail Series;Almost Certain Convergence;Convergence in Probability