论文标题
具有顶点级波动的图形值的过程
Graphon-valued processes with vertex-level fluctuations
论文作者
论文摘要
我们考虑一类图形值随机过程，其中每个顶点的类型随着时间的流逝而随机波动。总体而言，顶点的路径在给定时间之前类型确定了当时边缘有效或不活动的概率。我们的重点是在极限中相关的经验图形的演变，因为顶点的数量倾向于无穷大，而在图形值过程中的波动更可能是由顶点类型中的波动引起的，而不是由于这些类型的边缘状态的波动而引起的。我们得出了样品路径大偏差原理和随机过程的收敛性。我们通过处理一类随机过程来证明我们的方法的灵活性，在这些过程中，边缘概率不仅取决于顶点类型的波动，还取决于图形本身的状态。
We consider a class of graph-valued stochastic processes in which each vertex has a type that fluctuates randomly over time. Collectively, the paths of the vertex types up to a given time determine the probabilities that the edges are active or inactive at that time. Our focus is on the evolution of the associated empirical graphon in the limit as the number of vertices tends to infinity, in the setting where fluctuations in the graph-valued process are more likely to be caused by fluctuations in the vertex types than by fluctuations in the states of the edges given these types. We derive both sample-path large deviation principles and convergence of stochastic processes. We demonstrate the flexibility of our approach by treating a class of stochastic processes where the edge probabilities depend not only on the fluctuations in the vertex types but also on the state of the graph itself.
