The relation between strong mixing and conditionally strong mixing is answered by examples,that is,the strong mixing property of random variables does not imply the conditionally strong mixing property,and the opposit...The relation between strong mixing and conditionally strong mixing is answered by examples,that is,the strong mixing property of random variables does not imply the conditionally strong mixing property,and the opposite implication is also not true.Some equivalent definitions and basic properties of conditional 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 non-conditional case.展开更多
基金supported by National Natural Science Foundation of China (GrantNo. 11126333)the Natural Science Foundation Project of Chongqing (Grant No. 2009BB2370)the SCRof Chongqing Municipal Education Commission (Grant Nos. KJ120731 and KJ100726)
文摘The relation between strong mixing and conditionally strong mixing is answered by examples,that is,the strong mixing property of random variables does not imply the conditionally strong mixing property,and the opposite implication is also not true.Some equivalent definitions and basic properties of conditional 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 non-conditional case.
