Poincaré Type Inequalities for the Mixed Poisson Measures

Mathematics – Probability

Scientific paper

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Scientific paper

By using the Mecke identity, we study a class of birth-death type Dirichlet
forms for the mixed Poisson measure. Then the Poincar\'{e} inequality and the
weak Poincar\'{e} inequality are established for the birth-death type Dirichlet
form. Moreover, a Poincar\'{e} type inequality is disproved under some
reasonable assumptions.

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