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Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Speed of convergence to equilibrium in Wasserstein metrics for Kac-like kinetic equations
2.	Creator	Author's name, affiliation, country	Federico Bassetti; University of Pavia; Italy
2.	Creator	Author's name, affiliation, country	Eleonora Perversi; University of Pavia; Italy
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Boltzmann-like equations, Kac caricature, smoothing transformation, stable laws, rate of convergence to equilibrium, Wasserstein distances
3.	Subject	Subject classification	60B10; 82C40; 60E07; 60F05
4.	Description	Abstract	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2013-01-11
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2054
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-2054
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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