英文标题：
《SPDE limit of the global fluctuations in rank-based models》
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作者：
Praveen Kolli, Mykhaylo Shkolnikov
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最新提交年份：
2016
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英文摘要：
  We consider systems of diffusion processes (\"particles\") interacting through their ranks (also referred to as \"rank-based models\" in the mathematical finance literature). We show that, as the number of particles becomes large, the process of fluctuations of the empirical cumulative distribution functions converges to the solution of a linear parabolic SPDE with additive noise. The coefficients in the limiting SPDE are determined by the hydrodynamic limit of the particle system which, in turn, can be described by the porous medium PDE. The result opens the door to a thorough investigation of large equity markets and investment therein. In the course of the proof we also derive quantitative propagation of chaos estimates for the particle system.
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中文摘要：
我们考虑扩散过程系统（“粒子”）通过其秩相互作用（在数学金融文献中也称为“基于秩的模型”）。我们证明，随着粒子数的增加，经验累积分布函数的涨落过程收敛于一个带加性噪声的线性抛物型SPDE的解。极限SPDE中的系数由粒子系统的流体动力极限确定，而流体动力极限又可以用多孔介质PDE来描述。这一结果为彻底调查大型股票市场及其投资打开了大门。在证明过程中，我们还推导了粒子系统混沌估计的定量传播。
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics        数学
二级分类：Analysis of PDEs        偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE\'s, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
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一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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