高效反Z$变换和维纳-霍普夫因式分解

arXiv - QuantFin - Computational Finance Pub Date : 2024-04-30 DOI:arxiv-2404.19290

Svetlana Boyarchenko, Sergei Levendorskiĭ

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引用次数: 0

摘要

我们根据积分等值线的正弦变形、相应的变量变化和简化梯形法则，提出了与单位圆上函数的 Z$ 变换和维纳-霍普夫因式分解的数值反演密切相关的新方法。作为应用，我们考虑了概率分布高矩的评估和因果滤波器的构建。在具有中等特性的 Mac 上运行 Matlab 程序，分别在几十微秒和几毫秒内达到了 E-14 和 E-11 的精度。

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Efficient inverse $Z$-transform and Wiener-Hopf factorization

We suggest new closely related methods for numerical inversion of $Z$-transform and Wiener-Hopf factorization of functions on the unit circle, based on sinh-deformations of the contours of integration, corresponding changes of variables and the simplified trapezoid rule. As applications, we consider evaluation of high moments of probability distributions and construction of causal filters. Programs in Matlab running on a Mac with moderate characteristics achieves the precision E-14 in several dozen of microseconds and E-11 in several milliseconds, respectively.

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arXiv - QuantFin - Computational Finance

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