论文标题
在波动的赫尔夫里奇表面上的Langevin动力学的粗糙均质化
Rough homogenization for Langevin dynamics on fluctuating Helfrich surfaces
论文作者
论文摘要
在本文中，我们研究了langevin动力学在准平面波动的helfrich表面上的空间和时间上的不同规模限制。邓肯，埃利奥特，Pavliotis和Stuart（2015）的工作已经证明了该过程的收敛结果。我们通过证明ITô和Stratonovich粗糙路径提升的融合来扩展这项工作。对于粗糙的路径限制，通常会出现迭代积分的区域校正项，以及在Stratonovich迭代积分的某些方向上。这产生了有关均质化极限的其他信息，并使通过在粗糙的路径拓扑中使用iTô-Laneons映射的连续性在膜上驱动的扩散结果得出结论。
In this paper, we study different scaling rough path limit regimes in space and time for the Langevin dynamics on a quasi-planar fluctuating Helfrich surfaces. The convergence results of the processes were already proven in the work by Duncan, Elliott, Pavliotis and Stuart (2015). We extend this work by proving the convergence of the Itô and Stratonovich rough path lift. For the rough path limit, there appears, typically, an area correction term to the Itô iterated integrals, and in certain regimes to the Stratonovich iterated integrals. This yields additional information on the homogenization limit and enables to conclude on homogenization results for diffusions driven by the Brownian motion on the membrane using the continuity of the Itô-Lyons map in rough paths topology.
