The Law of the Iterated Logarithm over a Stationary Gaussian Sequence of Random Vectors

Miguel A. Arcones ()
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Miguel A. Arcones: Binghamton University

Journal of Theoretical Probability, 1999, vol. 12, issue 3, 615-641

Abstract: 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 $$(n{\text{ 2 log log }}n{\text{)}}^{{\text{ - 1/2}}} \sum\limits_{j{\text{ }} = {\text{ }}1}^n {(G(X_j ) - E[{\text{ }}G} (X_j )])$$ where G is a real function defined on ℝ d 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.

Keywords: Long range dependence; stationary Gaussian sequence; law of the iterated logarithm (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021667529846

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