Small ball probabilities of Gaussian fields

DOI10.1007/BF01198847zbMath0833.60043OpenAlexW2066464850MaRDI QIDQ1898837

Yanyan Li

Publication date: 5 March 1996

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01198847

zbMATH Keywords

Brownian sheetsmall ball probabilityGaussian fieldLevy fractional Brownian field

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Strong limit theorems (60F15) Self-similar stochastic processes (60G18)

Related Items (15)

Small ball probabilities of Gaussian fields ⋮ Small ball probabilities for a Wiener process under weighted sup-norms, with an application to the supremum of Bessel local times ⋮ THE EXIT PROBABILITIES OF BROWNIAN MOTION WITH VARIABLE DIMENSION APPLYING TO THE CONTROL OF POPULATION GROWTH ⋮ Some liminf results on increments of fractional Brownian motion ⋮ Some small ball probabilities for Gaussian processes under nonuniform norms ⋮ On the fractal nature of increments of the infinite series of OU processes related to the Chung LIL ⋮ Metric entropy of integration operators and small ball probabilites for the Brownian sheet ⋮ Increments and sample path properties of Gaussian processes ⋮ Properties of local-nondeterminism of Gaussian and stable random fields and their applications ⋮ A fractional Brownian field indexed by \(L^2\) and a varying Hurst parameter ⋮ Chung-type law of the iterated logarithm on \(l^p\)-valued Gaussian processes ⋮ The moduli of non-differentiability for Gaussian random fields with stationary increments ⋮ Two different kinds of liminfs on the LIL for two-parameter Wiener processes ⋮ Chung’s law for integrated Brownian motion ⋮ A Gaussian correlation inequality and its applications to the existence of small ball constant.

Cites Work

• A note on small ball probability of a Gaussian process with stationary increments
• Probability estimates for multiparameter Brownian processes
• Small ball estimates for Gaussian processes under Sobolev type norms
• New Gaussian estimates for enlarged balls
• Metric entropy and the small ball problem for Gaussian measures
• On almost sure limit inferior for \(B\)-valued stochastic processes and applications
• The small ball problem for the Brownian sheet
• Small values of Gaussian processes and functional laws of the iterated logarithm
• Small ball probabilities for Gaussian processes with stationary increments under Hölder norms
• Small ball probabilities of Gaussian fields
• On Certain Inequalities for Normal Distributions and their Applications to Simultaneous Confidence Bounds
• On Multivariate Normal Probabilities of Rectangles: Their Dependence on Correlations
• Unnamed Item
• Unnamed Item

This page was built for publication: Small ball probabilities of Gaussian fields