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January, 1987 The Central Limit Theorem for Stochastic Processes
N. T. Andersen, V. Dobric
Ann. Probab. 15(1): 164-177 (January, 1987). DOI: 10.1214/aop/1176992262

Abstract

If $f = \{f_t\mid t \in T\}$ is a centered, second-order stochastic process with bounded sample paths, it is then known that $f$ satisfies the central limit theorem in the topology of uniform convergence if and only if the intrinsic metric $\rho^2_f$ (on $T$) induced by $f$ is totally bounded and the normalized sums are eventually uniformly $\rho^2_f$-equicontinuous. We show that a centered, second-order stochastic process satisfies the central limit theorem in the topology of uniform convergence if and only if it has bounded sample paths and there exists totally bounded pseudometric $\rho$ on $T$ so that the normalized sums are eventually uniformly $\rho$-equicontinuous.

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N. T. Andersen. V. Dobric. "The Central Limit Theorem for Stochastic Processes." Ann. Probab. 15 (1) 164 - 177, January, 1987. https://doi.org/10.1214/aop/1176992262

Information

Published: January, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0615.60008
MathSciNet: MR877596
Digital Object Identifier: 10.1214/aop/1176992262

Subjects:
Primary: 60B12
Secondary: 60F05

Keywords: central limit theorem , eventual boundedness , eventual tightness , eventual uniform equicontinuity , Stochastic processes

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 1 • January, 1987
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