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Martingale central limit theorems without uniform asymptotic negligibility: Corrigendum

Published online by Cambridge University Press:  17 April 2009

R.J. Adler  and
D.J. Scott
R.J. Adler
Affiliation:
School of Mathematics, University of New South Wales, Kensington, New South Wales;
D.J. Scott
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria.
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The following is a correct proof of the main theorem of [1]. It should be substituted for the published Section 3, which, as pointed out by Professor B.L.S. Prakasa Rao, contains an error in the equations following (15) on page 49.

Type
Corrigendum
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 2 , April 1978 , pp. 311 - 319
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Adler, R.J. and Scott, D.J., “Martingale central limit theorems without uniform asymptotic negligibility”, Bull. Austral. Math. Soc. 13 (1975), 45–55.CrossRefGoogle Scholar
[2]Billingsley, Patrick, Convergence of probability measures (John Wiley & Sons, New York, London, Sydney, Toronto, 1968).Google Scholar
[3]Brown, B.M., “Martingale central limit theorems”, Ann. Math. Statist. 42 (1971), 59–66.CrossRefGoogle Scholar
[4]Feller, William, An introduction to probability theory and its applications, Volume I, 3rd ed. (John Wiley & Sons, New York, London, Sydney, 1968).Google Scholar
[5]McLeish, D.L., “Dependent central limit theorems and invariance principles”, Ann. Probability 2 (1974), 620–628.CrossRefGoogle Scholar
[6]Scott, D.J., “Central limit theorems for martingales and for processes with stationary increments using a Skorokhod representation approach”, Adv. in Appl. Probability 5 (1973), 119–137.CrossRefGoogle Scholar