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Central Limit Theorems for Interchangeable Processes

Published online by Cambridge University Press:  20 November 2018

J. R. Blum
Affiliation:
Indiana University
H. Chernoff
Affiliation:
Stanford University
M. Rosenblatt
Affiliation:
Purdue University
H. Teicher
Affiliation:
Purdue University
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Let {Xn} (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 i1, i2, H3 … , ik, the joint distribution of

depends merely on k and is independent of the integers i1, i2, … , ik. 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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1958

References

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