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arXiv · 0906.2280

A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature

Aldéric Joulin
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Abstract

The purpose of this paper is to extend the investigation of Poisson-type deviation inequalities started by Joulin (Bernoulli 13 (2007) 782--798) to the empirical mean of positively curved Markov jump processes. In particular, our main result generalizes the tail estimates given by Lezaud (Ann. Appl. Probab. 8 (1998) 849--867, ESAIM Probab. Statist. 5 (2001) 183--201). An application to birth--death processes completes this work.

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Aldéric Joulin. 2009-06-12. A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature. https://doi.org/10.3150/08-bej158

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