Large deviations for the solution of a Kac-type kinetic equation

Federico Bassetti; Lucia Ladelli

doi:10.3934/krm.2013.6.245

Article Contents

2013, Volume 6, Issue 2: 245-268. Doi: 10.3934/krm.2013.6.245

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Large deviations for the solution of a Kac-type kinetic equation

Federico Bassetti^1, and
Lucia Ladelli^2,

1.
Dipartimento di Matematica, Università degli Studi di Pavia, Via Ferrata 1, 27100, Pavia
2.
Dipartimento di Matematica, Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133, Milanod

Received: October 2012

Revised: November 2012

Published: June 2013

Abstract / Introduction Related Papers Cited by

Abstract

The aim of this paper is to study large deviations for the self-similar solution of a Kac-type kinetic equation. Under the assumption that the initial condition belongs to the domain of normal attraction of a stable law of index $\alpha < 2$ and under suitable assumptions on the collisional kernel, precise asymptotic behavior of the large deviations probability is given.

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Mathematics Subject Classification: Primary: 60F10; Secondary: 82C40, 60F05.

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