Abstract
Criteria for the super-Poincaré inequality and the weak-Poincaré inequality about ergodic birth-death processes are presented. Our work further completes ten criteria for birth-death processes presented in Table 1.4 (p. 15) of Prof. Mu-Fa Chen’s book “Eigenvalues, Inequalities and Ergodic Theory” (Springer, London, 2005). As a byproduct, we conclude that only ergodic birth-death processes on finite state space satisfy the Nash inequality with index 0 < ν ≤ 2.
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Supported by Natural Science Foundation of Fujian Province (Grant No. 2010J05002)
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Wang, J. Criteria for super- and weak-Poincaré inequalities of ergodic birth-death processes. Acta. Math. Sin.-English Ser. 28, 357–370 (2012). https://doi.org/10.1007/s10114-012-9737-7
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DOI: https://doi.org/10.1007/s10114-012-9737-7
Keywords
- Super-Poincaré inequality
- weak-Poincaré inequality
- Nash inequality
- ergodic birth-death processes
- capacity