标记根图上随机过程的熵概念
A Notion of Entropy for Stochastic Processes on Marked Rooted Graphs
摘要：
在本文中，我们引入了标记根图上的随机过程的熵的概念。为此，我们采用局部弱极限理论的稀疏标记图的框架，也被称为客观的方法，由于Benjamini，Schramm，Aldous，Steele和Lyons。我们的贡献是一个推广的概念熵介绍了由Bordenave和Caputo的图形进行标记在他们的顶点和边缘。时间序列理论是驱动控制理论、通信、信息论和信号处理等领域的大量应用的引擎。可以预期的是，由组合结构（特别是图）索引的平稳随机过程理论最终会产生类似的广泛影响。
英文摘要：
In this document, we introduce a notion of entropy for stochastic processes on marked rooted graphs. For this, we employ the framework of local weak limit theory for sparse marked graphs, also known as the objective method, due to Benjamini, Schramm, Aldous, Steele and Lyons. Our contribution is a generalization of the notion of entropy introduced by Bordenave and Caputo to graphs which carry marks on their vertices and edges. The theory of time series is the engine driving an enormous range of applications in areas such as control theory, communications, information theory and signal processing. It is to be expected that a theory of stationary stochastic processes indexed by combinatorial structures, in particular graphs, would eventually have a similarly wide-ranging impact.
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