Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-07-01T12:33:34.516Z Has data issue: false hasContentIssue false
  • English
  • Français

ALMOST SURE CONVERGENCES IN THE LAW OF LARGE NUMBERS

Published online by Cambridge University Press:  25 September 2003

KAORU YONEDA  and
Shigeru Takahashi
KAORU YONEDA
Affiliation:
Department of Mathematics and Information Sciences, Osaka Prefecture University, Sakai, Osaka, [email protected]
Get access

Abstract

The integrability of a control function of the almost sure convergence $$ \displaystyle\lim_{n \to \infty}\frac{X_1(\omega)+X_2(\omega)+\ldots+X_n(\omega)}{T_n}, $$ where $T_n \,{\uparrow}\, \infty $ as $n \to \infty$ and $X_1,X_2,\cdots,X_n,\cdots $ are independent identically distributed random variables, is studied.

Keywords

60F17 (primary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 2 , October 2003 , pp. 527 - 544
Copyright
The London Mathematical Society 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)