Complete convergence and complete moment convergence for martingale difference sequence

Authors
Wang, Xue Jun
Citation
Wang, Xue Jun, Complete convergence and complete moment convergence for martingale difference sequence, Acta mathematica Sinica. English series (Print) , 30(1), 2014, pp. 119-132
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
30
Issue
1
Year of publication
2014
Pages
119 - 132
Database
ACNP
SICI code
Abstract
In the paper, we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale difference sequence. Especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for martingale difference sequence. As an application, a strong law of large numbers for martingale difference sequence is obtained.