On the Tail Series Laws of Large Numbers for Independent Random Elements in Banach Spaces

Banach 공간에서 독립인 확률요소들의 Tail 합에 대한 대수의 법칙에 대하여

  • Nam Eun-Woo (Department of Computer Science and Statistics Air Force Academy)
  • 남은우 (공군사관학교 전산통계학과)
  • Published : 2006.05.01

Abstract

For the almost certainly convergent series $S_n=\sum_{i=1}^nV-i$ of independent random elements in Banach spaces, by investigating tail series laws of large numbers, the rate of convergence of the series $S_n$ to a random variable s is studied in this paper. More specifically, by studying the duality between the limiting behavior of the tail series $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$ of random variables and that of Banach space valued random elements, an alternative way of proving a result of the previous work, which establishes the equivalence between the tail series weak law of large numbers and a limit law, is provided in a Banach space setting.

Keywords

Rate of Convergence;Series of Random Elements in Banach Space;Tail Series;Strong Law of Large Numbers;Weak Law of Large Numbers