Spectral gap and convex concentration inequalities for birth-death processes

DOI10.1214/07-AIHP149zbMath1172.60023OpenAlexW2058756531MaRDI QIDQ838304

Wei Liu, Yu Tao Ma

Publication date: 24 August 2009

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/78021

zbMATH Keywords

spectral gapPoisson equationbirth-death processLipschitz functionconvex concentration inequality

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Continuous-time Markov processes on discrete state spaces (60J27)

Related Items (10)

Spectral gap, isoperimetry and concentration on trees ⋮ Convex concentration for some additive functionals of jump stochastic differential equations ⋮ Transport-information inequalities for Markov chains ⋮ A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature ⋮ Lipschitzian norms and functional inequalities for birth-death processes ⋮ Intertwining and commutation relations for birth-death processes ⋮ New point view of spectral gap in functional spaces for birth-death processes ⋮ The equilibrium states of large networks of Erlang queues ⋮ On Stein's factors for Poisson approximation in Wasserstein distance with nonlinear transportation costs ⋮ Computable Bounds on the Spectral Gap for Unreliable Jackson Networks

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