Bulletin of the
Korean Mathematical Society
BKMS
Article
ALL ARTICLES
View
Bull. Korean Math. Soc. 1999; 36(2): 305-314
Printed June 1, 1999
Copyright © The Korean Mathematical Society.
On the Pruss extension of the Hsu-Robbins-Erdos theorem
Soo Hak Sung
Pai Chai University
The Hsu-Robbins-Erd\H os theorem states that if $\{X_n,$ $n\ge 1\}$ is a sequence of independent and identically distributed random variables, then $EX_1^20.$ Under some auxiliary conditions, Sp\u ataru (1994) extended this to the case where the $X_n$ are independent, but their distributions come from a finite set. Pruss (1996) proved Sp\u ataru's result under weaker conditions. The purpose of this paper is to improve Pruss conditions.
Keywords: complete convergence, strong law, sums of independent random variables
MSC numbers: 60F15
Article Tools
Stats or Metrics
Share this article on :
Related articles in BKMS
-
On complete convergence for weighted sums of i.i.d. random variables with application to moving average processes
2009; 46(4): 617-626
-
On a Spitzer-type law of large numbers for partial sums of independent and identically distributed random variables under sub-linear expectations
2023; 60(3): 687-703
-
On complete convergence for weighted sums of coordinatewise negatively associated random vectors in Hilbert spaces
2022; 59(4): 879-895
-
Convergence properties for the partial sums of widely orthant dependent random variables under some integrable assumptions and their applications
2020; 57(6): 1451-1473
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd