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In this paper, weak Poincaré inequalities are obtained for convolution probabilities with explicit rate functions by constructing suitable Lyapunov functions. Here, one of these Lyapunov functions is introduced for the… Click to show full abstract
In this paper, weak Poincaré inequalities are obtained for convolution probabilities with explicit rate functions by constructing suitable Lyapunov functions. Here, one of these Lyapunov functions is introduced for the first time and can be used to improve parts of results on the estimate of rate functions for super Poincaré inequalities 13 as well. In addition, these weak Poincaré inequalities are applied to some concrete examples, which can refine some of results even for the case without convolution.
Journal Title: Infinite Dimensional Analysis, Quantum Probability and Related Topics
Year Published: 2019
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