Standard

Small ball probabilities for gaussian random fields and tensor products of compact operators. / Karol, Andrei; Nazarov, Alexander; Nikitin, Yakov.

In: Transactions of the American Mathematical Society, Vol. 360, No. 3, 01.03.2008, p. 1443-1474.

Research output: Contribution to journal › Article › peer-review

Harvard

Karol, A, Nazarov, A & Nikitin, Y 2008, 'Small ball probabilities for gaussian random fields and tensor products of compact operators', Transactions of the American Mathematical Society, vol. 360, no. 3, pp. 1443-1474. https://doi.org/10.1090/S0002-9947-07-04233-X

APA

Karol, A., Nazarov, A., & Nikitin, Y. (2008). Small ball probabilities for gaussian random fields and tensor products of compact operators. Transactions of the American Mathematical Society, 360(3), 1443-1474. https://doi.org/10.1090/S0002-9947-07-04233-X

Vancouver

Karol A, Nazarov A, Nikitin Y. Small ball probabilities for gaussian random fields and tensor products of compact operators. Transactions of the American Mathematical Society. 2008 Mar 1;360(3):1443-1474. https://doi.org/10.1090/S0002-9947-07-04233-X

Author

Karol, Andrei ; Nazarov, Alexander ; Nikitin, Yakov. / Small ball probabilities for gaussian random fields and tensor products of compact operators. In: Transactions of the American Mathematical Society. 2008 ; Vol. 360, No. 3. pp. 1443-1474.

BibTeX

@article{d20cfd6b127b4e8b985d7f8dca5e95b7,
title = "Small ball probabilities for gaussian random fields and tensor products of compact operators",
abstract = "We find the logarithmic L2-small ball asymptotics for a large class of zero mean Gaussian fields with covariances having the structure of {"}tensor product{"}. The main condition imposed on marginal covariances is the regular behavior of their eigenvalues at infinity that is valid for a multitude of Gaussian random functions including the fractional Brownian sheet, Ornstein - Uhlenbeck sheet, etc. So we get the far-reaching generalizations of well-known results by Cs{\'a}ki (1982) and by Li (1992). Another class of Gaussian fields considered is the class of additive fields studied under the supremum-norm by Chen and Li (2003). Our theorems are based on new results on spectral asymptotics for the tensor products of compact self-adjoint operators in Hilbert space which are of independent interest.",
keywords = "Brownian sheet, Fractional Brownian motion, Ornstein - Uhlenbeck sheet, Slowly varying functions, Small deviations, Spectral asymptotics, Tensor product of operators",
author = "Andrei Karol and Alexander Nazarov and Yakov Nikitin",
year = "2008",
month = mar,
day = "1",
doi = "10.1090/S0002-9947-07-04233-X",
language = "English",
volume = "360",
pages = "1443--1474",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "3",

}

RIS

TY - JOUR

T1 - Small ball probabilities for gaussian random fields and tensor products of compact operators

AU - Karol, Andrei

AU - Nazarov, Alexander

AU - Nikitin, Yakov

PY - 2008/3/1

Y1 - 2008/3/1

N2 - We find the logarithmic L2-small ball asymptotics for a large class of zero mean Gaussian fields with covariances having the structure of "tensor product". The main condition imposed on marginal covariances is the regular behavior of their eigenvalues at infinity that is valid for a multitude of Gaussian random functions including the fractional Brownian sheet, Ornstein - Uhlenbeck sheet, etc. So we get the far-reaching generalizations of well-known results by Csáki (1982) and by Li (1992). Another class of Gaussian fields considered is the class of additive fields studied under the supremum-norm by Chen and Li (2003). Our theorems are based on new results on spectral asymptotics for the tensor products of compact self-adjoint operators in Hilbert space which are of independent interest.

AB - We find the logarithmic L2-small ball asymptotics for a large class of zero mean Gaussian fields with covariances having the structure of "tensor product". The main condition imposed on marginal covariances is the regular behavior of their eigenvalues at infinity that is valid for a multitude of Gaussian random functions including the fractional Brownian sheet, Ornstein - Uhlenbeck sheet, etc. So we get the far-reaching generalizations of well-known results by Csáki (1982) and by Li (1992). Another class of Gaussian fields considered is the class of additive fields studied under the supremum-norm by Chen and Li (2003). Our theorems are based on new results on spectral asymptotics for the tensor products of compact self-adjoint operators in Hilbert space which are of independent interest.

KW - Brownian sheet

KW - Fractional Brownian motion

KW - Ornstein - Uhlenbeck sheet

KW - Slowly varying functions

KW - Small deviations

KW - Spectral asymptotics

KW - Tensor product of operators

UR - http://www.scopus.com/inward/record.url?scp=44649094637&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-07-04233-X

DO - 10.1090/S0002-9947-07-04233-X

M3 - Article

AN - SCOPUS:44649094637

VL - 360

SP - 1443

EP - 1474

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 3

ER -

ID: 36071854