Conditional central limit theorems for a sequence of conditional independent random variables

Abstract

A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but no necessarily conditionally identically distributed random variables is establtished. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability. © 2014 The Korean Mathematical Society.