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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, Japanyoneda@mi.cias.osakafu-u.ac.jp
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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

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