Law of Iterated Logarithm for Weighted Sums of Functionals of Long-Memory Gaussian Sequences
Abstract
We prove iterated-logarithm results for weighted nonlinear functionals of long-memory stationary Gaussian sequences with regularly varying weights. The leading Hermite chaos determines the natural almost-sure scale. In the linear case we obtain the sharp variance-normalized LIL constant. In the nonlinear fixed-chaos regime we identify the weighted functional cluster set and obtain a variational formula for the nonlinear LIL constant.
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