摘要翻译：
通过数值模拟，我们证实了引入帕累托定律的Takayasu-Sato-Takayasu(TST)模型满足Gibrat定律下的详细平衡。在模拟中，我们取一个指数帐篷形函数作为增长率分布。我们还从数值上证实了与TST模型中给出Pareto指数$\mu$的方程等价的反射定律。此外，我们在非直布罗特定律下对模型进行了扩展，修正了随机系数。在该模型中，还对详细的平衡进行了数值观察。所得pdf在大尺度直布罗陀定律区为幂律分布，在中尺度非直布罗陀定律区为对数正态分布。这些都在数值模拟中得到了准确的证实。
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英文标题：
《Non-Gibrat's law in the middle scale region》
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作者：
Masashi Tomoyose, Shouji Fujimoto and Atushi Ishikawa
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最新提交年份：
2008
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分类信息：

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。
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
  By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the equation which gives the Pareto index $\mu$ in TST model. Moreover, we extend the model modifying the stochastic coefficient under a Non-Gibrat's law. In this model, the detailed balance is also numerically observed. The resultant pdf is power-law in the large scale Gibrat's law region, and is the log-normal distribution in the middle scale Non-Gibrat's one. These are accurately confirmed in the numerical simulation.
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PDF链接：
https://arxiv.org/pdf/0809.3060