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.
Citation
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
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