Abstract
Explicit rate of convergence in variance (or more general entropies) is obtained for a class of Piecewise Deterministic Markov Processes such as the TCP process, relying on functional inequalities. A method to establish Poincaré (and more generally Beckner) inequalities with respect to a diffusion-type energy for the invariant law of such hybrid processes is developed.
Citation
Pierre Monmarché. "On $\mathcal{H}^1$ and entropic convergence for contractive PDMP." Electron. J. Probab. 20 1 - 30, 2015. https://doi.org/10.1214/EJP.v20-3581
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