一个通用的随机传播模型
A versatile stochastic dissemination model
摘要：
本文考虑了一个高度一般的传播模型，跟踪财富分布的随机演化在一组代理。有两种类型的事件：（i）财富单位外部到达，（ii）财富单位在代理之间重新分配，而在整个马尔可夫调制是允许的。我们推导出一个系统的耦合微分方程描述的联合瞬态分布的代理人的财富值，转化为线性微分方程时，考虑相应的手段和（协）方差。虽然我们的模型使用了财富分配给代理人的（经济）术语，但我们通过一系列例子说明它可以更广泛地使用。事实上，它还有助于分析意见在人群中的传播（从而推广现有的意见动态模型），以及分析文件存储系统的动态（从而允许评估存储策略的有效性）。
英文摘要：
This paper consider a highly general dissemination model that keeps track of the stochastic evolution of the distribution of wealth over a set of agents. There are two types of events: (i) units of wealth externally arrive, and (ii) units of wealth are redistributed among the agents, while throughout Markov modulation is allowed. We derive a system of coupled differential equations describing the joint transient distribution of the agents' wealth values, which translate into linear differential equations when considering the corresponding means and (co-)variances. While our model uses the (economic) terminology of wealth being distributed over agents, we illustrate through a series of examples that it can be used considerably more broadly. Indeed, it also facilitates the analysis of the spread of opinions over a population (thus generalizing existing opinion dynamics models), and the analysis of the dynamics of a file storage system (thus allowing the assessment of the efficacy of storage policies).
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