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$L_2$-Small Deviations for Weighted Stationary Processes (1705.00422v2)
Published 1 May 2017 in math.PR
Abstract: We find logarithmic asymptotics of $L_2$-small deviation probabilities for weighted stationary Gaussian processes (both for real and complex-valued) having power-type discrete or continuous spectrum. As in the recent work by Hong, Lifshits and Nazarov, our results are based on the spectral theory of pseudo-differential operators developed by Birman and Solomyak.