$L_2$-Small Deviations for Weighted Stationary Processes

Mikhail Lifshits; Alexander Nazarov

doi:10.1112/s0025579317000572

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arXiv · 1705.00422

$L_2$-Small Deviations for Weighted Stationary Processes

Mikhail Lifshits·Alexander Nazarov

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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.

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Mikhail Lifshits, Alexander Nazarov. 2017-05-01. $L_2$-Small Deviations for Weighted Stationary Processes. https://doi.org/10.1112/s0025579317000572

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