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ONE DIMENSIONAL CRITICAL KINETIC FOKKER-PLANCK EQUATIONS, BESSEL AND STABLE PROCESSES

Abstract : We consider a particle moving in one dimension, its velocity being a reversible diffusion process, with constant diffusion coefficient, of which the invariant measure behaves like (1 + |v|) −β for some β > 0. We prove that, under a suitable rescaling, the position process resembles a Brownian motion if β ≥ 5, a stable process if β ∈ [1, 5) and an integrated symmetric Bessel process if β ∈ (0, 1). The critical cases β = 1 and β = 5 require special rescalings. We recover some results of [24, 10, 19] and [1] with an alternative approach.
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https://hal.archives-ouvertes.fr/hal-01799460
Contributor : Camille Tardif <>
Submitted on : Thursday, May 24, 2018 - 5:33:23 PM
Last modification on : Friday, April 10, 2020 - 5:13:37 PM
Document(s) archivé(s) le : Saturday, August 25, 2018 - 2:56:33 PM

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  • HAL Id : hal-01799460, version 1

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Nicolas Fournier, Camille Tardif. ONE DIMENSIONAL CRITICAL KINETIC FOKKER-PLANCK EQUATIONS, BESSEL AND STABLE PROCESSES. 2018. ⟨hal-01799460⟩

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