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

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

2009-06-12

arxiv.org/abs/0906.2280v1

Bernoulli 2009, Vol. 15, No. 2, 532-549

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ158 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ158

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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