L2-SMALL DEVIATIONS FOR WEIGHTED STATIONARY PROCESSES

Михаил Анатольевич Лифшиц; Александр Ильич Назаров

doi:10.1112/S0025579317000572

L2-SMALL DEVIATIONS FOR WEIGHTED STATIONARY PROCESSES

Михаил Анатольевич Лифшиц, Александр Ильич Назаров

Research output

Abstract

We find logarithmic asymptotics of -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.

Translated title of the contribution	Малые уклонения в L_2 взвешенных стационарных процессов
Original language	English
Pages (from-to)	387-405
Number of pages	19
Journal	Mathematika
Volume	64
Issue number	2
DOIs	https://doi.org/10.1112/S0025579317000572 https://doi.org/10.1112/S0025579317000572
Publication status	Published - 2018

Scopus subject areas

Mathematics(all)

Access to Document

Fingerprint Dive into the research topics of 'L2-SMALL DEVIATIONS FOR WEIGHTED STATIONARY PROCESSES'. Together they form a unique fingerprint.

Cite this

@article{17fbbe75c5de4e1fbd2329a3d714eac5,

title = "L2-SMALL DEVIATIONS FOR WEIGHTED STATIONARY PROCESSES",

abstract = "We find logarithmic asymptotics of -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.",

keywords = "малые уклонения случайных процессов",

author = "Лифшиц, {Михаил Анатольевич} and Назаров, {Александр Ильич}",

year = "2018",

doi = "10.1112/S0025579317000572",

language = "English",

volume = "64",

pages = "387--405",

journal = "Mathematika",

issn = "0025-5793",

publisher = "Cambridge University Press",

number = "2",

}

TY - JOUR

T1 - L2-SMALL DEVIATIONS FOR WEIGHTED STATIONARY PROCESSES

AU - Лифшиц, Михаил Анатольевич

AU - Назаров, Александр Ильич

PY - 2018

Y1 - 2018

N2 - We find logarithmic asymptotics of -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.

AB - We find logarithmic asymptotics of -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.

KW - малые уклонения случайных процессов

UR - http://www.scopus.com/inward/record.url?scp=85054163404&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/l2small-deviations-weighted-stationary-processes

U2 - 10.1112/S0025579317000572

DO - 10.1112/S0025579317000572

M3 - Article

VL - 64

SP - 387

EP - 405

JO - Mathematika

JF - Mathematika

SN - 0025-5793

IS - 2

ER -