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摘要翻译：
传统的宏观经济动态模型从根本上说是不正确的。其原因在于对无穷小量分析的特殊性的误解。然而，即使是上述模型所设想的那些类型的解决方案，在反映现实的意义上也不具有代表性。很明显，线性微分方程理论的技术在这里是不够的。因此，科学家们的注意力转向了非线性微分方程理论。同时，平衡以及相应的具有矩阵性质的模型客观上是经济系统所固有的。为了把这个模型简化为微分形式，存在着被证明是无人主张的相当基本的方法。宏观经济论调--加速器的力量，需求的滞后，等等--伴随着大量抽象系数的使用而盛行。然而，矩阵和非线性微分方程之间并不存在有机的相互联系。相反，可以说积分方程的线性理论起源于矩阵分析。证明了具有参数相关核的第二类Fredholm线性积分方程在这类可能解方面具有较强的代表性。它似乎可以用来描述经济的任何曲折。为此要付出的代价是现有理论的非琐碎性。
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英文标题：
《The Problem of Modelling of Economic Dynamics in Differential Form》
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作者：
S. I. Chernyshov, V. S. Ponomarenko, and A. V. Voronin
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最新提交年份：
2008
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分类信息：
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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一级分类：Mathematics 数学
二级分类：Classical Analysis and ODEs 经典分析与颂歌
分类描述：Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics
特殊函数、正交多项式、调和分析、Ode、微分关系、变分法、逼近、展开、渐近
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一级分类：Mathematics 数学
二级分类：Dynamical Systems 动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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英文摘要：
Traditional models of macroeconomic dynamics are fundamentally incorrect. The reason lies in a misunderstanding of peculiarities of the analysis of infinitesimal quantities. However, even those types of solutions that are envisaged by the above-mentioned models are nonrepresentative in the sense of the reflection of realities. It became obvious that the techniques of the theory of linear differential equations were insufficient here. Accordingly, the scientists' attention switched to the theory of nonlinear differential equations. At the same time, balance and, accordingly, the model with matrix properties are objectively inherent in the economic system. For the reduction of this model to a differential form, there exist rather elementary means that proved to be unclaimed. Macroeconomic rhetoric - the power of the accelerator, a lag on the part of demand, etc. - accompanied by the use of a lot of abstract coefficients prevailed. However, there is no organic interrelation between matrix and nonlinear differential equations. On the contrary, it can be said that linear theory of integral equations originated in matrix analysis. The Fredholm linear integral equation of the second kind with a parameter-dependent kernel proves to be rather representative with regard to the class of possible solutions. It seems that it can be used for the description of any zigzags of the economy. The price one has to pay for this is the nontriviality of existing theory.
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PDF链接：
https://arxiv.org/pdf/0804.3658
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