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.
Publié le : 1974-10-14
Classification:
Gaussian process,
sample function,
Caratheodory property,
determinism,
window field,
local time,
60G15,
60G17
@article{1176996560,
author = {Berman, Simeon M.},
title = {A Gaussian Paradox: Determinism and Discontinuity of Sample Functions},
journal = {Ann. Probab.},
volume = {2},
number = {6},
year = {1974},
pages = { 950-953},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996560}
}
Berman, Simeon M. A Gaussian Paradox: Determinism and Discontinuity of Sample Functions. Ann. Probab., Tome 2 (1974) no. 6, pp. 950-953. http://gdmltest.u-ga.fr/item/1176996560/