A CLT for Empirical Processes Involving Time Dependent Data

Details A CLT for Empirical Processes Involving Time Dependent Data A CLT for Empirical Processes Involving Time Dependent Data

2010-08-16

arxiv.org/abs/1008.2697v1

Mathematics

Probability

Scientific paper

For stochastic processes $\{X_t: t \in E\}$, we establish sufficient conditions for the empirical process based on $\{ I_{X_t \le y} - P(X_t \le y): t \in E, y \in \mathbb{R}\}$ 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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