arXiv:1705.00422 Abstract | arXiv Analytics

arXiv:1705.00422 [math.PR]Abstract References Reviews Resources

$L_2$-Small Deviations for Weighted Stationary Processes

Published 2017-05-01Version 1

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.

Categories: math.PR

Subjects: 60G15, 60G10, 60G22, 47G30

Keywords: weighted stationary processes, small deviation probabilities, weighted stationary gaussian processes, logarithmic asymptotics, power-type discrete

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