## The Annals of Applied Probability

### Translated Poisson approximation using exchangeable pair couplings

#### Abstract

It is shown that the method of exchangeable pairs introduced by Stein [Approximate Computation of Expectations (1986) IMS, Hayward, CA] for normal approximation can effectively be used for translated Poisson approximation. Introducing an additional smoothness condition, one can obtain approximation results in total variation and also in a local limit metric. The result is applied, in particular, to the anti-voter model on finite graphs as analyzed by Rinott and Rotar [Ann. Appl. Probab. 7 (1997) 1080–1105], obtaining the same rate of convergence, but now for a stronger metric.

#### Article information

Source
Ann. Appl. Probab., Volume 17, Number 5-6 (2007), 1596-1614.

Dates
First available in Project Euclid: 3 October 2007

https://projecteuclid.org/euclid.aoap/1191419177

Digital Object Identifier
doi:10.1214/105051607000000258

Mathematical Reviews number (MathSciNet)
MR2358635

Zentralblatt MATH identifier
1143.60020

#### Citation

Röllin, Adrian. Translated Poisson approximation using exchangeable pair couplings. Ann. Appl. Probab. 17 (2007), no. 5-6, 1596--1614. doi:10.1214/105051607000000258. https://projecteuclid.org/euclid.aoap/1191419177

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