论文标题
一个平均原理，用于随机流和非对称迪里奇的收敛性
An averaging principle for stochastic flows and convergence of non-symmetric Dirichlet forms
论文作者
论文摘要
我们研究了歧管上确定性流动的时间变化的随机扰动。在接近Mosco-Convergence的意义上，使用非对称的Dirichlet形式及其收敛性，我们证明，随着确定性流的加速，法律中的扩散过程会收敛到在不同空间上定义的扩散。该平均原理也保持在流量的水平。我们在本文中的贡献包括：证明内核随机流的原始原理的证明；在不同空间上定义的非对称双线性形式序列的融合的定义和研究；在公制图或“书籍”上对加权Sobolev空间的研究。
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".
