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October, 1981 Lipschitz Smoothness and Convergence with Applications to the Central Limit Theorem for Summation Processes
Roy V. Erickson
Ann. Probab. 9(5): 831-851 (October, 1981). DOI: 10.1214/aop/1176994311

Abstract

We prove that certain jump summation processes converge in distribution for the uniform topology to the Brownian sheet, while smoothed summation processes converge for various Lipschitz topologies. These results follow after a careful study of abstract, generalized Lipschitz spaces. Along the way we affirm a conjecture about smoothness and continuity of processes defined on $\lbrack 0, 1\rbrack^d$.

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Roy V. Erickson. "Lipschitz Smoothness and Convergence with Applications to the Central Limit Theorem for Summation Processes." Ann. Probab. 9 (5) 831 - 851, October, 1981. https://doi.org/10.1214/aop/1176994311

Information

Published: October, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0473.60005
MathSciNet: MR628876
Digital Object Identifier: 10.1214/aop/1176994311

Subjects:
Primary: 60B10
Secondary: 60G17, 60G50

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 5 • October, 1981
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