Variational formulas of Poincaré-type inequalities for birth-death processes.

DOI10.1007/s10114-003-0308-9zbMath1040.60064OpenAlexW2001949004MaRDI QIDQ1421063

Chen Mu-Fa

Publication date: 2003

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-003-0308-9

zbMATH Keywords

logarithmic Sobolev inequalityOrlicz spacePoincaré inequalitybirth-death processNash inequalityvariational formula

Mathematics Subject Classification ID

Related Items (9)

Criteria for super- and weak-Poincaré inequalities of ergodic birth-death processes ⋮ Zero biasing and a discrete central limit theorem ⋮ Speed of stability for birth-death processes ⋮ Large time behaviors of upwind schemes and $B$-schemes for Fokker-Planck equations on $\mathbb {R}$ by jump processes ⋮ Unified speed estimation of various stabilities ⋮ Hypercontractivity for a quantum Ornstein-Uhlenbeck semigroup ⋮ Binomial-Poisson entropic inequalities and the M/M/∞queue ⋮ Capacitary criteria for Poincaré-type inequalities ⋮ On \(F\)-Sobolev and Orlicz-Sobolev inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Hardy-Littlewood theory for semigroups
• Upper bounds for symmetric Markov transition functions
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Nash inequalities for Markov processes in dimension one
• Explicit bounds of the first eigenvalue.
• Variational formulas and approximation theorems for the first eigenvalue in dimension one
• Variational formulas of Poincaré-type inequalities in Banach spaces of functions on the line.
• Analytic proof of dual variational formula for the first eigenvalue in dimension one
• Sobolev inequalities in disguise

This page was built for publication: Variational formulas of Poincaré-type inequalities for birth-death processes.