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
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
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