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June, 1979 Local Sample Path Properties of Gaussian Fields
Loren D. Pitt, Lanh Tat Tran
Ann. Probab. 7(3): 477-493 (June, 1979). DOI: 10.1214/aop/1176995048

Abstract

A zero-one law is derived for a class of Gaussian fields $\{X(t) : t \in R^d\}$ including the generalized multiparameter Brownian motion. Under very general conditions, the joint distribution of the suprema of several Gaussian processes defined over compact metric spaces is shown to be absolutely continuous with a bounded density. Sufficient conditions are given for the existence of proper scaling limits of $\{X(t)\}$. The results are then combined to study local oscillations and local maxima.

Citation

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Loren D. Pitt. Lanh Tat Tran. "Local Sample Path Properties of Gaussian Fields." Ann. Probab. 7 (3) 477 - 493, June, 1979. https://doi.org/10.1214/aop/1176995048

Information

Published: June, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0401.60035
MathSciNet: MR528325
Digital Object Identifier: 10.1214/aop/1176995048

Subjects:
Primary: 60G15
Secondary: 60J55

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 3 • June, 1979
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