Open Access
March 2013 A CLT for empirical processes involving time-dependent data
James Kuelbs, Thomas Kurtz, Joel Zinn
Ann. Probab. 41(2): 785-816 (March 2013). DOI: 10.1214/11-AOP711


For stochastic processes $\{X_{t} : t\in E\}$, we establish sufficient conditions for the empirical process based on $\{I_{X_{t}\le y}-\operatorname{Pr} (X_{t}\le y) : t\in E,y\in\mathbb{R}\}$ to satisfy the CLT uniformly in $t\in E$, $y\in\mathbb{R}$. Corollaries of our main result include examples of classical processes where the CLT holds, and we also show that it fails for Brownian motion tied down at zero and $E=[0,1]$.


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James Kuelbs. Thomas Kurtz. Joel Zinn. "A CLT for empirical processes involving time-dependent data." Ann. Probab. 41 (2) 785 - 816, March 2013.


Published: March 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1287.60034
MathSciNet: MR3077526
Digital Object Identifier: 10.1214/11-AOP711

Primary: 60F05
Secondary: 60F17

Keywords: central limit theorems , Empirical processes

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 2 • March 2013
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