Multivariate approximation in total variation, I: Equilibrium distributions of Markov jump processes

AD Barbour; MJ Luczak; A Xia

Journal article

Multivariate approximation in total variation, I: Equilibrium distributions of Markov jump processes

AD Barbour, MJ Luczak, A Xia

Annals of Probability | INST MATHEMATICAL STATISTICS | Published : 2018

DOI: 10.1214/17-AOP1204

Abstract

For integer valued random variables, the translated Poisson distributions form a flexible family for approximation in total variation, in much the same way that the normal family is used for approximation in Kolmogorov distance. Using the Stein-Chen method, approximation can often be achieved with error bounds of the same order as those for the CLT. In this paper, an analogous theory, again based on Stein's method, is developed in the multivariate context. The approximating family consists of the equilibrium distributions of a collection of Markov jump processes, whose analogues in one dimension are the immigration-death processes with Poisson distributions as equilibria. The method is illus..

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University of Melbourne Researchers

Andrew Barbour Author

Aihua Xia Author

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Grants

Awarded by Engineering and Physical Sciences Research Council

Funding Acknowledgements

[ "Work begun while ADB was Saw Swee Hock Professor of Statistics at the National University of Singapore, carried out in part at the University of Melbourne and at Monash University, and supported in part by Australian Research Council Grants Nos. DP120102728, DP120102398, DP150101459 and DP150103588.", "Work carried out in part at the University of Melbourne, and supported by an EPSRC Leadership Fellowship, grant reference EP/J004022/2, and in part by Australian Research Council Grants Nos. DP120102398 and DP150101459.", "Work supported in part by Australian Research Council Grants Nos. DP120102398 and DP150101459." ]