Open Access
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


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.


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Jack Cuzick. "Local Nondeterminism and the Zeros of Gaussian Processes." Ann. Probab. 6 (1) 72 - 84, February, 1978.


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

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

Primary: 60G17
Secondary: 60G15 , 60G25

Keywords: curve crossings , Gaussian processes , Local nondeterminism , Point processes , prediction , Zero crossings

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 1 • February, 1978
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