The Annals of Probability

Probability Estimates for Multiparameter Brownian Processes

Richard F. Bass

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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 $P(\sup_{t \in \lbrack 0, 1\rbrack^d}|W_F(t) - G(t)| \leq \varepsilon)$.

Article information

Source
Ann. Probab., Volume 16, Number 1 (1988), 251-264.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991899

Digital Object Identifier
doi:10.1214/aop/1176991899

Mathematical Reviews number (MathSciNet)
MR920269

Zentralblatt MATH identifier
0645.60044

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60F10: Large deviations 60G60: Random fields 62G10: Hypothesis testing

Keywords
Brownian sheet Kolmogorov-Smirnov large deviations Haar functions empirical processes

Citation

Bass, Richard F. Probability Estimates for Multiparameter Brownian Processes. Ann. Probab. 16 (1988), no. 1, 251--264. doi:10.1214/aop/1176991899. https://projecteuclid.org/euclid.aop/1176991899


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