标题： 半马尔可夫图动力学 显示英文标题

标题： Semi-Markov Graph Dynamics

摘要： 在本文中，我们概述了一个基于两个要素的图（或网络）动态模型。 第一个要素是在可能图空间上的马尔可夫链。 第二个要素是一种更新类型的半马尔可夫计数过程。 该模型包括将马尔可夫链与半马尔可夫计数过程进行子ordination。 换句话说，这意味着链的转移发生在称为时刻点的随机时间点。 该模型非常丰富，其与代数几何的可能联系被简要讨论。 此外，为了简化起见，我们专注于具有固定节点数的无向图空间。 然而，在一个例子中，我们提出了一个银行间市场模型，其中使用有向图甚至加权图是有意义的。 显示英文摘要

摘要： In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs.