Abstract
We present some optimal conditions for the compact law of the iterated logarithm of a sequence of jointly Gaussian processes in different situations. We also discuss the local law of the iterated logarithm for Gaussian processes indexed by arbitrary index sets, in particular for self-similar Gaussian processes. We apply these results to obtain the law of the iterated logarithm for compositions of Gaussian processes.
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Research partially supported by NSF Grant DMS-93-02583.
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Arcones, M.A. On the law of the iterated logarithm for Gaussian processes. J Theor Probab 8, 877–903 (1995). https://doi.org/10.1007/BF02410116
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DOI: https://doi.org/10.1007/BF02410116