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

1 December 1977

journal article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 14 (4) , 758-775
https://doi.org/10.2307/3213349

Abstract

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

Keywords

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