Time-changes of stochastic processes associated with resistance forms
Time-changes of stochastic processes associated with resistance forms
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DOI：
10.1214/17-ejp99
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
D. Croydon;B. Hambly;T. Kumagai
中科院分区：
文献类型：
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作者：
D. Croydon;B. Hambly;T. Kumagai
给定一个序列的电阻形式，收敛的Gromov-Hausdorff-vague拓扑，并满足一致的体积加倍条件，我们证明了相应的布朗运动和局部时的收敛性。作为其推论，我们获得了时变过程的收敛性。我们的主要结果的例子包括刘维布朗运动的标度极限，布绍陷阱模型和随机电导模型的树木和自相似分形。对于后两个模型，我们表明，在某些假设下的限制过程是一个FIN扩散的相关空间。
Given a sequence of resistance forms that converges with respect to the Gromov-Hausdorff-vague topology and satisfies a uniform volume doubling condition, we show the convergence of corresponding Brownian motions and local times. As a corollary of this, we obtain the convergence of time-changed processes. Examples of our main results include scaling limits of Liouville Brownian motion, the Bouchaud trap model and the random conductance model on trees and self-similar fractals. For the latter two models, we show that under some assumptions the limiting process is a FIN diffusion on the relevant space.