Large Deviations for the solution of a Kac-type kinetic equation
Federico Bassetti, Lucia Ladelli
TL;DR
This paper investigates the large deviations behavior of solutions to a Kac-type kinetic equation, focusing on self-similar solutions with initial conditions attracted to stable laws, providing precise asymptotic probabilities.
Contribution
It offers the first detailed analysis of large deviations for self-similar solutions of Kac-type kinetic equations under stable law attraction.
Findings
Asymptotic behavior of large deviations probabilities is characterized.
Results depend on the stable law index .
Provides conditions on the collisional kernel for large deviations analysis.
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 and under suitable assumptions on the collisional kernel, precise asymptotic behavior of the large deviations probability is given.
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