Some preliminary results on conditionally psi-mixing sequences of random variables

摘要

From the ordinary notion of psi-mixing for a sequence of random variables, a new concept called conditionally psi-mixing is proposed. That conditionally psi-mixing neither implies nor is implied by psi-mixing is illustrated by examples. Certain criteria for checking conditionally psi-mixing property as well as basic properties are derived, and several conditional covariance inequalities are obtained. By means of these properties and inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established.