The Annals of Probability

Multivariate approximation in total variation, II: Discrete normal approximation

A. D. Barbour, M. J. Luczak, and A. Xia

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Abstract

The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in $\mathbb{Z}^{d}$. We illustrate the use of the method for sums of independent integer valued random vectors, and for random vectors exhibiting an exchangeable pair. We conclude with an application to random colourings of regular graphs.

Article information

Source
Ann. Probab., Volume 46, Number 3 (2018), 1405-1440.

Dates
Received: December 2016
First available in Project Euclid: 12 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.aop/1523520020

Digital Object Identifier
doi:10.1214/17-AOP1205

Mathematical Reviews number (MathSciNet)
MR3785591

Zentralblatt MATH identifier
06894777

Subjects
Primary: 62E17: Approximations to distributions (nonasymptotic)
Secondary: 62E20: Asymptotic distribution theory 60J27: Continuous-time Markov processes on discrete state spaces 60C05: Combinatorial probability

Keywords
Markov population process multivariate approximation total variation distance infinitesimal generator Stein’s method

Citation

Barbour, A. D.; Luczak, M. J.; Xia, A. Multivariate approximation in total variation, II: Discrete normal approximation. Ann. Probab. 46 (2018), no. 3, 1405--1440. doi:10.1214/17-AOP1205. https://projecteuclid.org/euclid.aop/1523520020


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References

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