Variational Formulas of Poincaré-type Inequalities for Birth-Death Processes
Tóm tắt
In author’s one previous paper, the same topic was studied
for one dimensional diffusions. As a continuation, this paper
studies the discrete case, that is the birth-death processes.
The explicit criteria for the inequalities, the variational
formulas and explicit bounds of the corresponding constants in
the inequalities are presented. As typical applications, the
Nash inequalities and logarithmic Sobolev inequalities are
examined.
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