On a unified approach to the law of the iterated logarithm for martingales
- 1 June 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 14 (3) , 435-447
- https://doi.org/10.1017/s0004972700025363
Abstract
There are two distinct approaches in the literature to framing a version of the law of the iterated logarithm for martingales. One involves norming by constants, using the martingale variance and the other involves norming by random variables, using the sums of conditional variances of the increments, given their past. In this paper a portmanteau approach is provided, still based on the Skorokhod representation of the martingale, but involving normalization by more general random variables. This extends the functional forms of all the previously existing results.Keywords
This publication has 4 references indexed in Scilit:
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- Invariance Principles for the Law of the Iterated Logarithm for Martingales and Processes with Stationary IncrementsThe Annals of Probability, 1973
- A martingale analogue of Kolmogorov's law of the iterated logarithmProbability Theory and Related Fields, 1970
- An invariance principle for the law of the iterated logarithmProbability Theory and Related Fields, 1964