Comparison results for the lower tail of Gaussian seminorms

Li, Wenbo V.

doi:10.1007/bf01046776

Cited by 93 publications

(53 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…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).…”

supporting

confidence: 57%

Small ball probabilities for Gaussian random fields and tensor products of compact operators

Karol

Nazarov

Nikitin

2008

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. We find the logarithmic L 2 -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.

show abstract

supporting

confidence: 57%

Small ball probabilities for Gaussian random fields and tensor products of compact operators

Karol

Nazarov

Nikitin

2008

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Various generalizations of the above result are given in Li [Li92], Karol, Nazarov and Nikitin [K-03], Fill and Torcaso [FT04], and Gao and Li [GL04].…”

Section: For a Given Continuous Gaussian Random Field X(t) T ∈ [0 1]mentioning

confidence: 89%

Small ball probabilities for the Slepian Gaussian fields

Gao

2006

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. The d-dimensional Slepian Gaussian random field {S(t), t ∈ R d+ } is a mean zero Gaussian process with covariance function ES(s), and under the sup-norm on [0, 1] 2 which implies Talagrand's result for the Brownian sheet. The method of proof for the sup-norm case is purely probabilistic and analytic, and thus avoids ingenious combinatoric arguments of using decreasing mathematical induction. In particular, Riesz product techniques are new ingredients in our arguments.

show abstract

“…See Erickson [6], Li [12] and their combined references for many examples of when this assumption is valid.…”

Section: An Applicationmentioning

confidence: 99%