 Asymptotic behavior of a class of multiple time scales stochastic kinetic equationsCharles-Edouard Bréhier and Shmuel Rakotonirina-Ricquebourg Stochastic Processes and their Applications, 2024, vol. 168, issue C Abstract: We consider a class of stochastic kinetic equations, depending on two time scale separation parameters ɛ and δ: the evolution equation contains singular terms with respect to ɛ, and is driven by a fast ergodic process which evolves at the time scale t/δ2. We prove that when (ɛ,δ)→(0,0) the spatial density converges to the solution of a linear diffusion PDE. This result is a mixture of diffusion approximation in the PDE sense (with respect to the parameter ɛ) and of averaging in the probabilistic sense (with respect to the parameter δ). The proof employs stopping times arguments and a suitable new perturbed test functions approach which is adapted to consider the general regime ɛ≠δ. Keywords: Stochastic kinetic equations; Averaging principle; Diffusion approximation; Perturbed test functions method (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:168:y:2024:i:c:s0304414923002375 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2023.104265 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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