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Complete Convergence and Weak Law of Large Numbers for <i><span style="text-decoration:overline;">ρ</span></i>-Mixing Sequences of Random Variables
College of Science, Guilin University of Technology, Guilin, China
- 1 College of Science, Guilin University of Technology, Guilin, China
Open Journal of Statistics·Volume 02 (2012)·Pages 484–490·Published 13 December 2012·DOI10.4236/ojs.2012.25062
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Abstract
In this paper, the complete convergence and weak law of large numbers are established for ρ -mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ -mixing sequences of random variables without necessarily adding any extra conditions.
Keywords<i><span style="text-decoration:overline">ρ</span></i>-Mixing Sequence of Random VariablesComplete ConvergenceWeak Law of Large Number
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