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October, 1974 A Gaussian Paradox: Determinism and Discontinuity of Sample Functions
Simeon M. Berman
Ann. Probab. 2(5): 950-953 (October, 1974). DOI: 10.1214/aop/1176996560

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.

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Simeon M. Berman. "A Gaussian Paradox: Determinism and Discontinuity of Sample Functions." Ann. Probab. 2 (5) 950 - 953, October, 1974. https://doi.org/10.1214/aop/1176996560

Information

Published: October, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0292.60054
MathSciNet: MR375449
Digital Object Identifier: 10.1214/aop/1176996560

Subjects:
Primary: 60G15
Secondary: 60G17

Keywords: Caratheodory property , determinism , Gaussian process , Local time , sample function , window field

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 5 • October, 1974
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