Translator Disclaimer
June, 1977 Conditions for Sample-Continuity and the Central Limit Theorem
Marjorie G. Hahn
Ann. Probab. 5(3): 351-360 (June, 1977). DOI: 10.1214/aop/1176995796

Abstract

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.

Citation

Download Citation

Marjorie G. Hahn. "Conditions for Sample-Continuity and the Central Limit Theorem." Ann. Probab. 5 (3) 351 - 360, June, 1977. https://doi.org/10.1214/aop/1176995796

Information

Published: June, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0388.60043
MathSciNet: MR440679
Digital Object Identifier: 10.1214/aop/1176995796

Subjects:
Primary: 60G17
Secondary: 60F05

Rights: Copyright © 1977 Institute of Mathematical Statistics

JOURNAL ARTICLE
10 PAGES


SHARE
Vol.5 • No. 3 • June, 1977
Back to Top