An Averaging Principle for Stochastic Flows and Convergence of Non-Symmetric Dirichlet Forms.

Autor: Barret, Florent, Raimond, Olivier
Zdroj: Potential Analysis; Mar2022, Vol. 56 Issue 3, p483-548, 66p
Abstrakt: We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using non-symmetric Dirichlet forms and their convergence in a sense close to the Mosco-convergence, we prove that, as the deterministic flow is accelerated, the diffusion process converges in law to a diffusion defined on a different space. This averaging principle also holds at the level of the flows. Our contributions in this article include: a proof of an original averaging principle for stochastic flows of kernels; the definition and study of a convergence of sequences of non-symmetric bilinear forms defined on different spaces; the study of weighted Sobolev spaces on metric graphs or "books". [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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