Open Access
Translator Disclaimer
February, 1978 Local Nondeterminism and the Zeros of Gaussian Processes
Jack Cuzick
Ann. Probab. 6(1): 72-84 (February, 1978). DOI: 10.1214/aop/1176995611

Abstract

The concept of local nondeterminism introduced by Berman is generalized and applied to divided difference sequences generated by a Gaussian process. The resulting estimates are then used to find simple sufficient conditions for the finiteness of the moments of the number of crossings of level zero. In particular it is shown that under mild regularity conditions very little more is required to make all moments finite when the variance is finite. The results are extended to curves $\xi \in \mathscr{L}_2\lbrack 0, T\rbrack$. Finally examples are given in which the variance is finite but the third moment is infinite.

Citation

Download Citation

Jack Cuzick. "Local Nondeterminism and the Zeros of Gaussian Processes." Ann. Probab. 6 (1) 72 - 84, February, 1978. https://doi.org/10.1214/aop/1176995611

Information

Published: February, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0374.60051
MathSciNet: MR488252
Digital Object Identifier: 10.1214/aop/1176995611

Subjects:
Primary: 60G17
Secondary: 60G15, 60G25

Rights: Copyright © 1978 Institute of Mathematical Statistics

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.6 • No. 1 • February, 1978
Back to Top