SOME RESULTS ON CONDITIONALLY UNIFORMLY STRONG MIXING SEQUENCES OF RANDOM VARIABLES

Title & Authors
SOME RESULTS ON CONDITIONALLY UNIFORMLY STRONG MIXING SEQUENCES OF RANDOM VARIABLES
Yuan, De-Mei; Hu, Xue-Mei; Tao, Bao;

Abstract
From the ordinary notion of uniformly strong mixing for a sequence of random variables, a new concept called conditionally uniformly strong mixing is proposed and the relation between uniformly strong mixing and conditionally uniformly strong mixing is answered by examples, that is, uniformly strong mixing neither implies nor is implied by conditionally uniformly strong mixing. A couple of equivalent definitions and some of basic properties of conditionally uniformly strong mixing random variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established, which is a conditional version of the earlier result under the non-conditional case.
Keywords
conditionally uniformly strong mixing;conditional covariance inequality;conditional independence;conditional stationarity;conditional central limit theorem;conditional characteristic function;
Language
English
Cited by
1.
EXTENSIONS OF SEVERAL CLASSICAL RESULTS FOR INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES TO CONDITIONAL CASES,;;

대한수학회지, 2015. vol.52. 2, pp.431-445
1.
EXTENSIONS OF SEVERAL CLASSICAL RESULTS FOR INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES TO CONDITIONAL CASES, Journal of the Korean Mathematical Society, 2015, 52, 2, 431
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