摘要翻译：
本文发展了一种用于随机滤波的动量空间渐近展开技术。结果表明，用傅里叶变换结合非线性项的多项式函数逼近，得到了相应条件分布的常微分方程组。由于ODE系统的简单性，可以很容易地进行高阶计算。此外，用更新初始条件的小子周期顺序求解ODEs使得以数值有效的方式实现渐近展开的子步方法成为可能。这可以显着提高性能，否则逼近会严重失败。该方法有望为具有未观测参数的更加真实的金融建模以及涉及非线性测度值过程的问题提供一个有用的工具。
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英文标题：
《Momentum-Space Approach to Asymptotic Expansion for Stochastic Filtering》
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作者：
Masaaki Fujii
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最新提交年份：
2013
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分类信息：

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：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
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英文摘要：
  This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive system of ordinary differential equations (ODEs) for the relevant conditional distribution. Thanks to the simplicity of the ODE system, higher order calculation can be performed easily. Furthermore, solving ODEs sequentially with small sub-periods with updated initial conditions makes it possible to implement a substepping method for asymptotic expansion in a numerically efficient way. This is found to improve the performance significantly where otherwise the approximation fails badly. The method is expected to provide a useful tool for more realistic financial modeling with unobserved parameters, and also for problems involving nonlinear measure-valued processes.
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PDF链接：
https://arxiv.org/pdf/1209.1893