Strong Laws for Martingale Differences and Independent Random Variables

Henry Teicher

Journal of Theoretical Probability, 1998, vol. 11, issue 4, 979-995

Abstract: Abstract A strong law of large numbers (SLLN) for martingale differences {X n,ℱn,n≥1} permitting constant, random or hybrid normalizations, is obtained via a related SLLN for their conditional variances E{X n 2 |ℱn-1}n≥1. This, in turn, leads to martingale generalizations of known results for sums of independent random variables. Moreover, in the independent case, simple conditions are given for a generalized SLLN which contains the classical result of Kolmogorov when the variables are i.i.d.

Keywords: Strong laws; martingale differences; conditional variances (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022616915799

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