| Título: | Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations |
| Autores: |
Bassetti, Federico; University of Pavia Perversi, Eleonora; University of Pavia |
| Fecha: | 2013-01-04 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Boltzmann-like equations, Kac caricature, smoothing transformation, stable laws, rate of convergence to equilibrium, Wasserstein distances 60B10; 82C40; 60E07; 60F05 |
| Descripción: | This work deals with a class of one-dimensional measure-valued kinetic equations, which constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the domain of normal attraction of an $\alpha$-stable law, the solution of the equation converges weakly to a suitable scale mixture of centered $\alpha$-stable laws. In this paper we present explicit exponential rates for the convergence to equilibrium in Kantorovich-Wasserstein distancesof order $p>\alpha$, under the natural assumption that the distancebetween the initial datum and the limit distribution is finite. For $\alpha=2$ this assumption reduces to the finiteness of the absolute moment of order $p$ of the initial datum. On the contrary, when $\alpha<2$, the situation is more problematic due to the fact that both the limit distributionand the initial datum have infinite absolute moment of any order $p >\alpha$. For this case, we provide sufficient conditions for the finiteness of the Kantorovich-Wasserstein distance. |
| Idioma: | Inglés |
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