Diffusion limit for a stochastic kinetic problem with unbounded driving process

2020/09/22 by Shmuel Rakotonirina-Ricquebourg, Rakotonirina-Ricquebourg, Shmuel
Mathematics · #35R60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR #msc:35R60

paper · pdf · doi:10.48550/arxiv.2009.10406

57 pages

arxiv created 2021/06/25 · arxiv updated 2021/06/28

Abstract

This paper studies the limit of a kinetic evolution equation involving a small parameter and driven by a random process which also scales with the small parameter. In order to prove the convergence in distribution to the solution of a stochastic diffusion equation while removing a boundedness assumption on the driving random process, we adapt the method of perturbed test functions to work with stopped martingales problems.

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