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

Joulin, Aldéric

Bernoulli, Volume 15 (2009) no. 1, p. 532-549 / Harvested from Project Euclid

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 online : 2009-05-15
Classification: birth–death process, deviation inequality, empirical mean, Markov jump process, Wasserstein curvature

@article{1241444901,
     author = {Joulin, Ald\'eric},
     title = {A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature},
     journal = {Bernoulli},
     volume = {15},
     number = {1},
     year = {2009},
     pages = { 532-549},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1241444901}
}

Joulin, Aldéric. A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature. Bernoulli, Volume 15 (2009) no. 1, pp.  532-549. http://gdmltest.u-ga.fr/item/1241444901/