## The Annals of Probability

### Local Sample Path Properties of Gaussian Fields

#### 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.

#### Article information

Source
Ann. Probab., Volume 7, Number 3 (1979), 477-493.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176995048

Digital Object Identifier
doi:10.1214/aop/1176995048

Mathematical Reviews number (MathSciNet)
MR528325

Zentralblatt MATH identifier
0401.60035

JSTOR

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60J55: Local time and additive functionals

#### Citation

Pitt, Loren D.; Tran, Lanh Tat. Local Sample Path Properties of Gaussian Fields. Ann. Probab. 7 (1979), no. 3, 477--493. doi:10.1214/aop/1176995048. https://projecteuclid.org/euclid.aop/1176995048