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On central limit and iterated logarithm supplements to the martingale convergence theorem

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde
C. C. Heyde*
Affiliation:
C.S.I.R.O. Division of Mathematics and Statistics, Canberra
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Abstract

Let {Sn, n ≧ 1} be a zero, mean square integrable martingale for which so that Sn → S∞ a.s., say, by the martingale convergence theorem. The paper is principally concerned with obtaining central limit and iterated logarithm results for Bn(Sn – S∞) where the multipliers Bn ↑ ∞ a.s. An example on the Pólya urn scheme is given to illustrate the results.

Keywords

RATES OF CONVERGENCE: MARTINGALE CONVERGENCE THEOREMCENTRAL LIMIT THEOREMITERATED LOGARITHM LAWPÓLYA URN SCHEME
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 4 , December 1977 , pp. 758 - 775
Copyright
Copyright © Applied Probability Trust 1977 

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