英文标题：
《Spurious memory in non-equilibrium stochastic models of imitative
  behavior》
---
作者：
Vygintas Gontis, Aleksejus Kononovicius
---
最新提交年份：
2017
---
英文摘要：
  The origin of the long-range memory in the non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases a notion of spurious memory is introduced. A good example of Markov processes with spurious memory is stochastic process driven by a non-linear stochastic differential equation (SDE). This example is at odds with models built using fractional Brownian motion (fBm). We analyze differences between these two cases seeking to establish possible empirical tests of the origin of the observed long-range memory. We investigate probability density functions (PDFs) of burst and inter-burst duration in numerically obtained time series and compare with the results of fBm. Our analysis confirms that the characteristic feature of the processes described by a one-dimensional SDE is the power-law exponent $3/2$ of the burst or inter-burst duration PDF. This property of stochastic processes might be used to detect spurious memory in various non-equilibrium systems, where observed macroscopic behavior can be derived from the imitative interactions of agents.
---
中文摘要：
非平衡系统中长程记忆的起源仍然是一个悬而未决的问题，因为这种现象可以用基于马尔可夫过程的模型再现。在这些情况下，引入了伪内存的概念。具有虚假记忆的马尔可夫过程的一个很好的例子是由非线性随机微分方程（SDE）驱动的随机过程。这个例子与使用分数布朗运动（fBm）建立的模型不一致。我们分析这两种情况之间的差异，试图建立观察到的长程记忆起源的可能的实证检验。我们研究了数值获得的时间序列中突发和突发间持续时间的概率密度函数（PDF），并与fBm的结果进行了比较。我们的分析证实，一维SDE描述的过程的特征是脉冲串或脉冲串间持续时间PDF的幂律指数3/2。随机过程的这一特性可能被用来检测各种非平衡系统中的虚假记忆，在这些系统中，观察到的宏观行为可以从主体的模拟相互作用中衍生出来。
---
分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
--
一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
--

---
PDF下载：
-->