Let $\{X(t): t\in\lbrack 0, 1\rbrack\}$ be a stochastic process. For any function $f$ such that $E(X(t) - X(s))^2 \leqq f(|t - s|)$, a condition is found which implies that $X$ is sample-continuous and satisfies the central limit theorem in $C\lbrack 0, 1\rbrack$. Counterexamples are constructed to verify a conjecture of Garsia and Rodemich and to improve a result of Dudley.
Publié le : 1977-06-14
Classification:
Sample-continuity,
central limit theorems in $C\lbrack 0, 1 \rbrack$ and $D\lbrack 0, 1 \rbrack$,
second-order processes,
60G17,
60F05
@article{1176995796,
author = {Hahn, Marjorie G.},
title = {Conditions for Sample-Continuity and the Central Limit Theorem},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 351-360},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995796}
}
Hahn, Marjorie G. Conditions for Sample-Continuity and the Central Limit Theorem. Ann. Probab., Tome 5 (1977) no. 6, pp. 351-360. http://gdmltest.u-ga.fr/item/1176995796/