Central Limit Theorems for Interchangeable Processes

Abstract

Let { X n} ( n = 1, 2 , …) be a stochastic process. The random variables comprising it or the process itself will be said to be interchangeable if, for any choice of distinct positive integers i 1 , i 2 , H 3 … , i k , the joint distribution of depends merely on k and is independent of the integers i 1 , i 2 , … , i k . It was shown by De Finetti (3) that the probability measure for any interchangeable process is a mixture of probability measures of processes each consisting of independent and identically distributed random variables.