A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature
By A. Joulin. 2009
49 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/5a0dac7e41d7020407974d873832321d9e6d838f
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In Applied Mathematics
- Luigi Ambrosio
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- Giuseppe Savar'e
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Citations in the corpus
- Displacement convexity of entropy and related inequalities on graphs (2012, background): “However, while a lot is now known in the Riemannian setting (and more generally in geodesic spaces), very little is known so far in discrete spaces (such as finite graphs or finite Markov chains), with the notable exception of some notions of (discrete) Ricci curvature proposed recently by several a”
- Riemannian Ricci curvature lower bounds in metric measure spaces with -finite measure (2012, methodology): “This implies that RCD(K,∞) spaces have Ricci curvature bounded from below by K according to the W1-contractivity property taken as a definition in Ollivier [26] and Joulin [22].”
- Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes (2016, methodology): “Following ideas from [22,35,36], we show that Theorem 2.”
- CURVATURE, CONCENTRATION AND ERROR ESTIMATES FOR MARKOV CHAIN MONTE CARLO (2009, unknown): “The Annals of Probability 2010, Vol. 38, No. 6, 2418–2442 DOI: 10.1214/10-AOP541 © Institute of Mathematical Statistics, 2010”
- Exponential ergodicity for Markov processes with random switching (2013, background): “e notation δxPt(dy)=Pt(x,dy). To verify equation (1.3) is not much of a restriction because we do not assume that ρ(i)>0. The best constant in this inequality is called the Wasserstein curvaturein [26, 27] and the coarse Ricci curvature in [29, 30], since it is heavily related to the geometry of ”
- Metric measure spaces with Riemannian Ricci curvature bounded from below (2011, background): “This implies that RCD(K,∞) spaces have Ricci curvature bounded from below by K according to [37], [23].”