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Article Dans Une Revue Communications in Mathematical Physics Année : 2021

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

Résumé

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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Dates et versions

hal-01799460 , version 1 (24-05-2018)
hal-01799460 , version 2 (25-03-2021)

Identifiants

Citer

Nicolas Fournier, Camille Tardif. ONE DIMENSIONAL CRITICAL KINETIC FOKKER-PLANCK EQUATIONS, BESSEL AND STABLE PROCESSES. Communications in Mathematical Physics, 2021, 381 (1), pp.143-173. ⟨10.1007/s00220-020-03903-0⟩. ⟨hal-01799460v2⟩
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