Abstract
Let $F$ be a distribution function on $\lbrack 0, 1\rbrack^d$, and let $W_F$ be the Gaussian process that is the weak limit of the empirical process determined by $F$. If $G$ is a function on $\lbrack 0, 1\rbrack^d$, upper and lower bounds are found for $P(\sup_{t \in \lbrack 0, 1\rbrack^d}|W_F(t) - G(t)| \leq \varepsilon)$.
Citation
Richard F. Bass. "Probability Estimates for Multiparameter Brownian Processes." Ann. Probab. 16 (1) 251 - 264, January, 1988. https://doi.org/10.1214/aop/1176991899
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