Abstract
A sufficient condition is given for a sequence of partial-sum set-indexed processes with nonuniform $\phi$-mixing condition to converge to Brownian motion. The main result (Theorem 1.1) is an extension of the similar results of Goldie and Greenwood by weakening the $\phi$-mixing condition. An application (Corollary 4.2) to certain Gibbs fields is given.
Citation
Dongching Chen. "A Uniform Central Limit Theorem for Nonuniform $\phi$-Mixing Random Fields." Ann. Probab. 19 (2) 636 - 649, April, 1991. https://doi.org/10.1214/aop/1176990445
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