A Notion of Entropy for Stochastic Processes on Marked Rooted Graphs

A Notion of Entropy for Stochastic Processes on Marked Rooted Graphs
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标记根图上随机过程的熵概念

DOI：
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发表时间：
2019
期刊：
arXiv.org
影响因子：
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通讯作者：
V. Anantharam
V. Anantharam
中科院分区：
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文献类型：
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作者：
Payam Delgosha;V. Anantharam

文献摘要

被引文献

相似文献

本文引入了标记根图上随机过程的熵的概念。为此，我们采用了Benjamini， Schramm, Aldous， Steele和Lyons提出的稀疏标记图的局部弱极限理论框架，也称为客观方法。我们的贡献是将Bordenave和Caputo引入的熵的概念推广到顶点和边缘上带有标记的图。
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.