Journal of Applied Mathematics and Stochastic Analysis 
Volume 2005 (2005), Issue 1, Pages 55-66
doi:10.1155/JAMSA.2005.55

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

Abstract

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.