Poincaré and Weak Poincaré 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 Poincaré and weak Poincaré inequalities are established, while another Poincaré type inequality is disproved under some reasonable assumptions.

References in corpus (3)

• Stochastic analysis on configuration spaces: basic ideas and recent results
• The fractional Poisson measure in infinite dimensions
• Exponential Convergence Rates of Second Quantization Semigroups and Applications