# American Institute of Mathematical Sciences

June  2013, 6(2): 245-268. doi: 10.3934/krm.2013.6.245

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

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

Received  October 2012 Revised  November 2012 Published  February 2013

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.
Citation: Federico Bassetti, Lucia Ladelli. Large deviations for the solution of a Kac-type kinetic equation. Kinetic & Related Models, 2013, 6 (2) : 245-268. doi: 10.3934/krm.2013.6.245
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