Martingale central limit theorems without uniform asymptotic negligibility-Reference-Cited by-同舟云学术

Martingale central limit theorems without uniform asymptotic negligibility

Published:1975-08 Issue:1 Volume:13 Page:45-55
ISSN:0004-9727
Container-title:Bulletin of the Australian Mathematical Society
language:en
Short-container-title:Bull. Austral. Math. Soc.

Author:

Adler R.J.,Scott D.J.

Abstract

Central limit theorems are obtained for martingale arrays without the requirement of uniform asymptotic negligibility. The results obtained generalise the sufficiency part of Zolotarev's extension of the classical Lindeberg-Feller central limit theorem [V.M. Zolotarev, Theor. Probability Appl. 12 (1967), 608–618] and also the main martingale central limit theorem (not functional central limit theorem however) of D.L. McLeish [Ann. Probability 2 (1974), 620–628.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference7 articles.

1. A Generalization of the Lindeberg-Feller Theorem

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

3. Martingale Central Limit Theorems

4. Dependent Central Limit Theorems and Invariance Principles

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1. Principle of Conditioning in Limit Theorems for Sums of Random Variables;The Annals of Probability;1986-07-01

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3. Martingale central limit theorems without uniform asymptotic negligibility: Corrigendum;Bulletin of the Australian Mathematical Society;1978-04

4. A martingale central limit theorem without negligibility conditions;Bulletin of the Australian Mathematical Society;1978-02