LIPSCHITZIAN NORMS AND FUNCTIONAL INEQUALITIES FOR BIRTH-DEATH PROCESSES

被引：0
作者：
Liu, Wei [1 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2024年 / 29卷 / 05期
关键词：
Birth-death process; Poisson equation; transportation-information in-equality; concentration inequality; Cheeger-type isoperimetric inequality; TRANSPORTATION-INFORMATION INEQUALITIES; SPECTRAL GAP; LOGARITHMIC SOBOLEV; EIGENVALUE; ISOPERIMETRY;
D O I：
10.3934/dcdsb.2023177
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a birth-death process with generator L and reversible invariant probability measure pi. We identify explicitly the Lipschitzian norm of the solution of the Poisson equation -LG = g - pi(g) for |g| <= phi. This leads to some transportation-information inequalities, concentration inequalities and Cheeger-type isoperimetric inequalities. Several examples are provided to illustrate the results.
引用
收藏
页码：2282 / 2297
页数：16
相关论文
共 20 条
  • [1] Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincare
    Bakry, Dorninique
    Cattiaux, Patrick
    Guillin, Arnaud
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (03) : 727 - 759
  • [2] A note on Talagrand's transportation inequality and logarithmic Sobolev inequality
    Cattiaux, Patrick
    Guillin, Arnaud
    Wu, Li-Ming
    [J]. PROBABILITY THEORY AND RELATED FIELDS, 2010, 148 (1-2) : 285 - 304
  • [3] Lyapunov conditions for Super Poincare inequalities
    Cattiaux, Patrick
    Guillin, Arnaud
    Wang, Feng-Yu
    Wu, Liming
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (06) : 1821 - 1841
  • [4] Variational formulas and approximation theorems for the first eigenvalue in dimension one
    Chen, M
    [J]. SCIENCE IN CHINA SERIES A-MATHEMATICS, 2001, 44 (04): : 409 - 418
  • [5] Chen M.-F., 2004, From Markov chains to non-equilibrium particle systems, VSecond
  • [6] Chen M.-F., 2005, Eigenvalues, Inequalities, and Ergodic Theory (Probability and Its Applications)
  • [7] Analytic proof of dual variational formula for the first eigenvalue in dimension one
    Chen, MF
    [J]. SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 1999, 42 (08): : 805 - 815
  • [8] Explicit bounds of tbe first eigenvalue
    Chen, MF
    [J]. SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 2000, 43 (10): : 1051 - 1059
  • [9] Estimation of spectral gap for elliptic operators
    Chen, MF
    Wang, FY
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (03) : 1239 - 1267
  • [10] Chen Mufa, 1996, Acta Mathematica Sinica. New Series, V12, P337
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