Abstract
Let {X j } ∞j = 1 be a stationary Gaussian sequence of random vectors with mean zero. We give sufficient conditions for the compact law of the iterate logarithm of
where G is a real function defined on ℝd with finite second moment. Our result builds on Ho,(6) who proved an upper-half of the law of iterated logarithm for a sequence of random variables.
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Arcones, M.A. The Law of the Iterated Logarithm over a Stationary Gaussian Sequence of Random Vectors. Journal of Theoretical Probability 12, 615–641 (1999). https://doi.org/10.1023/A:1021667529846
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DOI: https://doi.org/10.1023/A:1021667529846