图上扩散过程收敛的一个判据
A Criterion for Convergence of Diffusion Processes on Graphs
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中文总结 AI 辅助
本文针对图上的扩散过程，利用尺度函数、速度函数及粘合条件参数，给出了过程族弱收敛的判据，推广了Freidlin和Wentzell在直线上的结果。
中文摘要 AI 辅助
本文研究图上的扩散过程。在第$i$条边上，每个过程由形如$D_{v_i}D^+_{u_i}$的算子控制，顶点处的行为由粘合条件决定。本文根据尺度函数和速度函数$u_i^n$与$v_i^n$以及粘合条件参数的行为，刻画了此类过程族向极限过程的弱收敛。这可视为Freidlin和Wentzell关于直线上过程族弱收敛结果的推广。
英文摘要
In this paper, we consider diffusion processes on a graph. On the $i$-th edge, each process is governed by an operator of the form $D_{v_i}D^+_{u_i}$, and the behavior at the vertices is determined by the gluing conditions. The paper characterizes the weak convergence of a family of such processes to a limiting process in terms of the behavior of the scale and speed functions $u_i^n$ and $v_i^n$ and the parameters of the gluing conditions. This may be viewed as a generalization of Freidlin and Wentzell's result on the weak convergence of a family of processes on a line.
发表机构
- University of Maryland（马里兰大学）
机构由 AI 辅助整理，请以论文原文为准。
