Potential Analysis ( IF 1.1 ) Pub Date : 2021-05-27 , DOI: 10.1007/s11118-020-09893-x Florent Barret , Olivier Raimond
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:
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a proof of an original averaging principle for stochastic flows of kernels;
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the definition and study of a convergence of sequences of non-symmetric bilinear forms defined on different spaces;
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the study of weighted Sobolev spaces on metric graphs or “books”.
中文翻译:
随机流和非对称Dirichlet形式的收敛性的平均原理
我们研究扩散过程和随机流,它们是流形上确定性流的随时间变化的随机扰动。使用非对称狄利克雷形式及其在某种意义上接近莫斯科收敛的收敛,我们证明,随着确定性流的加速,扩散过程在法律上收敛到定义在不同空间上的扩散。这种平均原则也适用于流量级别。我们在本文中的贡献包括:
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核随机流的原始平均原理的证明;
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在不同空间上定义的非对称双线性形式序列的收敛的定义和研究;
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度量图或“书籍”上的加权 Sobolev 空间的研究。