2020/03/17 by Florent Barret, Barret, Florent, Olivier Raimond +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2003.07587
openalex publication_date 2020/03/17 · openalex created_date 2021/06/22 · openalex updated_date 2026/07/28
We study diffusion processes and stochastic flows which are time-changed\nrandom perturbations of a deterministic flow on a manifold. Using non-symmetric\nDirichlet forms and their convergence in a sense close to the\nMosco-convergence, we prove that, as the deterministic flow is accelerated, the\ndiffusion process converges in law to a diffusion defined on a different space.\nThis averaging principle also holds at the level of the flows. Our\ncontributions in this article include: a proof of an original averaging\nprinciple for stochastic flows of kernels; the definition and study of a\nconvergence of sequences of non-symmetric bilinear forms defined on different\nspaces; the study of weighted Sobolev spaces on metric graphs or "books".\n