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

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.

Published in at http://dx.doi.org/10.3150/08-BEJ158 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (3)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions
• Poisson-type deviation inequalities for curved continuous-time Markov chains
• Deviation bounds for additive functionals of Markov process

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• Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians
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• Concentration inequalities in spaces of random configurations with positive Ricci curvatures