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2016 On strong embeddings by Stein’s method
Chinmoy Bhattacharjee, Larry Goldstein
Electron. J. Probab. 21: 1-30 (2016). DOI: 10.1214/16-EJP4299

Abstract

Strong embeddings, that is, couplings between a partial sum process of a sequence of random variables and a Brownian motion, have found numerous applications in probability and statistics. We extend Chatterjee’s novel use of Stein’s method for $\{-1,+1\}$ valued variables to a general class of discrete distributions, and provide $\log n$ rates for the coupling of partial sums of independent variables to a Brownian motion, and results for coupling sums of suitably standardized exchangeable variables to a Brownian bridge.

Citation

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Chinmoy Bhattacharjee. Larry Goldstein. "On strong embeddings by Stein’s method." Electron. J. Probab. 21 1 - 30, 2016. https://doi.org/10.1214/16-EJP4299

Information

Received: 13 May 2015; Accepted: 18 January 2016; Published: 2016
First available in Project Euclid: 25 February 2016

zbMATH: 1338.60064
MathSciNet: MR3485357
Digital Object Identifier: 10.1214/16-EJP4299

Subjects:
Primary: 60F05, 60F17, 60G09

JOURNAL ARTICLE
30 PAGES


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Vol.21 • 2016
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