The Annals of Probability

Lipschitz Smoothness and Convergence with Applications to the Central Limit Theorem for Summation Processes

Roy V. Erickson

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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 $\lbrack 0, 1\rbrack^d$.

Article information

Source
Ann. Probab., Volume 9, Number 5 (1981), 831-851.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994311

Digital Object Identifier
doi:10.1214/aop/1176994311

Mathematical Reviews number (MathSciNet)
MR628876

Zentralblatt MATH identifier
0473.60005

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60G17: Sample path properties 60G50: Sums of independent random variables; random walks

Keywords
Lipschitz spaces weak convergence central limit theorem summation processes

Citation

Erickson, Roy V. Lipschitz Smoothness and Convergence with Applications to the Central Limit Theorem for Summation Processes. Ann. Probab. 9 (1981), no. 5, 831--851. doi:10.1214/aop/1176994311. https://projecteuclid.org/euclid.aop/1176994311


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