Poincar\'e and Weak Poincar\'e Inequalities for the Mixed Poisson Measures
Abstract
By using the Mecke identity, we study a class of birth-death type Dirichlet forms associated with the mixed Poisson measure. Both Poincar\'e and weak Poincar\'e inequalities are established, while another Poincar\'e type inequality is disproved under some reasonable assumptions.
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