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Pré-Publication, Document De Travail Année : 2022

Fractional diffusion limit for a kinetic Fokker-Planck equation with diffusive boundary conditions in the half-line

Résumé

We consider a particle living in $\mathbb{R}_+$, whose velocity is a positive recurrent diffusion with heavy-tailed invariant distribution when the particle lives in $(0,\infty)$. When it hits the boundary $x=0$, the particle restarts with a random strictly positive velocity. We show that the properly rescaled position process converges weakly to a stable process reflected on its infimum.

Dates et versions

hal-03886146 , version 1 (06-12-2022)

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Loïc Béthencourt. Fractional diffusion limit for a kinetic Fokker-Planck equation with diffusive boundary conditions in the half-line. 2022. ⟨hal-03886146⟩
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