Abstract
Let {S n , n ≧ 1} be a zero, mean square integrable martingale for which \(\lim _{n \to \infty } ES_n^2 < \infty \) so that S n →S 221E; 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 221E;) where the multipliers B n ↑ ∞ a.s. An example on the P ólya urn scheme is given to illustrate the results.
Received in revised form 1 March 1977.
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Heyde, C.C. (2010). On Central Limit and Iterated Logarithm Supplements to the Martingale Convergence Theorem. In: Maller, R., Basawa, I., Hall, P., Seneta, E. (eds) Selected Works of C.C. Heyde. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5823-5_42
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