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$L_{2}$-SMALL DEVIATIONS FOR WEIGHTED STATIONARY PROCESSES

Part of: Integral, integro-differential, and pseudodifferential operators Stochastic processes

Published online by Cambridge University Press:  03 April 2018

Mikhail Lifshits  and
Alexander Nazarov
Mikhail Lifshits
Affiliation:
St. Petersburg State University, St. Petersburg, Universitetskii pr. 28, Russia MAI, Linköping University, Sweden email [email protected]
Alexander Nazarov
Affiliation:
St. Petersburg Department of Steklov Institute of Mathematics and St. Petersburg State University, St. Petersburg 191023, Russia email [email protected]
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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 a power-type discrete or continuous spectrum. Our results are based on the spectral theory of pseudo-differential operators developed by Birman and Solomyak.

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60G10: Stationary processes 60G22: Fractional processes, including fractional Brownian motion 47G30: Pseudodifferential operators
Type
Research Article
Information
Mathematika , Volume 64 , Issue 2 , 2018 , pp. 387 - 405
Copyright
Copyright © University College London 2018 

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