The Annals of Probability

A Gaussian Paradox: Determinism and Discontinuity of Sample Functions

Simeon M. Berman

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Abstract

A real stochastic process $\{X(t): 0 \leqq t \leqq 1\}$, is called window-deterministic if the points $(t, X(t))$ on its graph belonging to a "window" $\{(t, x): 0 \leqq t \leqq 1, a < x < b\}$ stochastically determine all other points on the graph. Here it is shown that a large class of Gaussian processes with discontinuous sample functions has this property.

Article information

Source
Ann. Probab., Volume 2, Number 5 (1974), 950-953.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996560

Digital Object Identifier
doi:10.1214/aop/1176996560

Mathematical Reviews number (MathSciNet)
MR375449

Zentralblatt MATH identifier
0292.60054

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G17: Sample path properties

Keywords
Gaussian process sample function Caratheodory property determinism window field local time

Citation

Berman, Simeon M. A Gaussian Paradox: Determinism and Discontinuity of Sample Functions. Ann. Probab. 2 (1974), no. 5, 950--953. doi:10.1214/aop/1176996560. https://projecteuclid.org/euclid.aop/1176996560


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