Abstract
Let G := (X 1,…,X n ) be a vector of standard Gaussian random variables. For a function H : ℝ → ℝ, we consider the normalized weighted H-sum of G, and under suitable hypotheses on G and H, we prove a Berry–Esséentype bound for it. We also prove a functional central limit theorem for a partial-sum process corresponding to such sums. The proof of the former theorem is based on a bound of the Kolmogorov distance between a random variable having a Wiener chaos representation and a standard normal random variable. These theorems extend the known results for the Hermite variations and are applied to several classes of Gaussian stochastic processes.
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This research was funded by a grant (No. MIP-053/2012) from the Research Council of Lithuania.
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Malukas, R. A Berry–Esséen bound for H-variation of a Gaussian process*. Lith Math J 56, 77–106 (2016). https://doi.org/10.1007/s10986-016-9306-3
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DOI: https://doi.org/10.1007/s10986-016-9306-3