Journal of Applied Mathematics and Stochastic Analysis
Volume 2005 (2005), Issue 1, Pages 55-66

Tauberian theorems for summability transforms

Rohitha Goonatilake

Department of Mathematical and Physical Sciences, Texas A&M International University, Laredo 78041-1900, TX, USA

Received 11 February 2004; Revised 9 July 2004

Copyright © 2005 Rohitha Goonatilake. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The convolution summability method is introduced as a generalization of the random-walk method. In this paper, two well-known summability analogs concerning the strong law of large numbers (SLLN) and the law of the single logarithm (LSL), that gives the rate of convergence in SLLN for the random-walk method, are extended to this generalized method.