Publication: Multivariate approximation in total variation, I: Equilibrium distributions of Markov jump processes
Multivariate approximation in total variation, I: Equilibrium distributions of Markov jump processes
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Barbour, A. D., Luczak, M. J., & Xia, A. (2018). Multivariate approximation in total variation, I: Equilibrium distributions of Markov jump processes. The Annals of Probability, 46(3), 1351–1404. https://doi.org/10.1214/17-aop1204
Abstract
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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 collect
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- Barbour, A D
- Luczak, M J
- Xia, A
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Citations
Barbour, A. D., Luczak, M. J., & Xia, A. (2018). Multivariate approximation in total variation, I: Equilibrium distributions of Markov jump processes. The Annals of Probability, 46(3), 1351–1404. https://doi.org/10.1214/17-aop1204
