Probability tails of Gaussian extrema

DOI10.1016/0304-4149(91)90072-KzbMath0728.60038OpenAlexW2070990830MaRDI QIDQ805058

Gennady Samorodnitsky

Publication date: 1991

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(91)90072-k

zbMATH Keywords

Gaussian processBrownian bridgeisonormal processset-indexed Brownian sheet

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Order statistics; empirical distribution functions (62G30) Sample path properties (60G17)

Related Items (19)

Gaussian-type upper bound for the evolution kernels on nilpotent meta-abelian groups ⋮ Extremal behavior of hitting a cone by correlated Brownian motion with drift ⋮ Extremes of Gaussian chaos processes with trend ⋮ On covariance functions with slowly or regularly varying modulo of continuity ⋮ Exceptional times and invariance for dynamical random walks ⋮ Extremes ofγ-reflected Gaussian processes with stationary increments ⋮ Extremes of Gaussian random fields with regularly varying dependence structure ⋮ Generalized Pickands constants and stationary max-stable processes ⋮ Monte Carlo estimates of extremes of stationary/nonstationary Gaussian processes ⋮ Random conformal weldings ⋮ Four finite dimensional (FD) surrogates for continuous random processes ⋮ Sojourn times of Gaussian processes with trend ⋮ On extreme value theory for group stationary Gaussian processes ⋮ Tail behaviour of Gaussian processes with applications to the Brownian pillow. ⋮ Accessing the power of tests based on set-indexed partial sums of multivariate regression residuals ⋮ Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes ⋮ Minima of \(H\)-valued Gaussian processes ⋮ On excursion sets, tube formulas and maxima of random fields. ⋮ Extremes of totally skewed \(\alpha \)-stable processes

Cites Work

• Regularity of Gaussian processes
• The supremum of a particular Gaussian field
• Estimation of first crossing time distribution for N-parameter Brownian motion processes relative to upper class boundaries
• Tail behaviour for suprema of empirical processes
• Tail behaviour for the suprema of Gaussian processes with applications to empirical processes
• Small tails for the supremum of a Gaussian process
• The Brunn-Minkowski inequality in Gauss space
• Distribution estimates for functionals of the two-parameter Wiener process
• The law of the iterated logarithm on arbitrary sequences for stationary Gaussian processes and Brownian motion
• Metric entropy of some classes of sets with differentiable boundaries
• The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
• Sample functions of the Gaussian process
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