On central limit and iterated logarithm supplements to the martingale convergence theorem
- 1 June 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 14 (04) , 758-775
- https://doi.org/10.1017/s0021900200105297
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
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