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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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