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Central limit theorems for martingales and for processes with stationary increments using a Skorokhod representation approach

Published online by Cambridge University Press:  01 July 2016

D. J. Scott
D. J. Scott*
Affiliation:
The Australian National University
*
∗Now at La Trobe University, Bundoora, Victoria.
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Abstract

The Skorokhod representation for martingales is used to obtain a functional central limit theorem (or invariance principle) for martingales. It is clear from the method of proof that this result may in fact be extended to the case of triangular arrays in which each row is a martingale sequence and the second main result is a functional central limit theorem for such arrays. These results are then used to obtain two functional central limit theorems for processes with stationary ergodic increments following on from the work of Gordin. The first of these theorems extends a result of Billingsley for Φ-mixing sequences.

Keywords

MARTINGALESCENTRAL LIMIT THEOREMINVARIANCE PRINCIPLETRIANGULAR ARRAYSSTATIONARY PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 1 , April 1973 , pp. 119 - 137
Copyright
Copyright © Applied Probability Trust 1973 

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