基于傅里叶级数展开式的有效期权定价方法

A novel option pricing method based on Fourier-cosine series expansion was proposed by Fang and Oosterlee. Developing their idea, three new option pricing methods based on Fourier, Fourier-cosine and Fourier-sine series expansions are presented in this paper, which are more efficient when the option prices are calculated with many strike prices. A series of numerical experiments under different exp-L~vy models are also given to compare these new methods with the Fang and Oosterlee＇s method and other methods.     

Klein-Gordon-Schrdinger方程的辛Fourier拟谱格式(英文)

主要讨论Klein-Gordon-Schrdinger方程的Fourier拟谱辛格式,包括中点公式和Strmer/Verlet格式.首先构造一个哈密尔顿方程,针对此哈密尔顿方程,在空间方向用Fourier拟谱离散得到一个有限维的哈密尔顿系统,对此有限维系统在时间方向用Strmer/Verlet方法离散得到KGS方程的完全显式的辛格式.中点格式虽然是隐式的但效率也很高,且具有质量守恒律.数值实验表明,辛格式能够在长时间内很好地模拟各类孤立波.     

MELLIN TRANSFORM IN WEAK FUNCTIONS AND MUENTS FORMULA

In this paper, the authors introduce some Mellin transforms in weak functions and discuss their applications to Mfints formula of the R.iemann zeta-function.     

窗口Fourier变换反演公式的级数表示——献给陆善镇教授75华诞

本文研究连续窗口Fourier变换的反演公式.与经典的积分重构公式不同,本文证明当窗函数满足合适的条件时,窗口Fourier变换的反演公式可以表示为一个离散级数.此外,本文还研究这一重构级数的逐点收敛及其在Lebesgue空间的收敛性.对于L^2空间,本文给出重构级数收敛的充分必要条件.     

非局部Kuramoto-Sivashinsky方程整体吸引子的维数估计

本文主要讨论NK-S方程整体吸引子的Hausdorff维数的上界估计.     

A method for detecting target echo in reverberation based on fractional Fourier transform

A method for detecting the target echo in reverberation was proposed based on fractional Fourier transform theory when the transmitted signal is linear frequency modulation signal. The slow time-varying envelope of reverberation is computed to process reverberation to be stationary. The stationary reverberation is cut into blocks using a sliding window. A narrow-band filter is applied in FrFT domain for each block and the signal is recovered through inverse FrFT. Output of the system is the energy of the recovered signal. When the target echo is included in one of the blocks, the reverberation noise is reduced, and the output is the energy of the target echo. All the simulation and lake experiment results show that the detection performance of the present method is better than that of the matched filter.     

一类二维空间中广义Boussinesq水波系统解的渐近性

在二维空间中，讨论了一类Boussinesq水波系统并用初值中出现的小参数的级数形式表示了此系统的确切解，得到了此解的长时间渐近行为按指数衰减．     

神经网络中的逼近问题

本文主要讨论径向基神经网络对函数，连续泛函及连续算子的逼近．     

热传导问题的一种近似解法

本文在给定的精度要求下,利用多项式及Fourier级数,给出了求热传导方程Cauchy问题在某处的近似解的方法,并把此方法推广成为求解任一有界域上满足给定精度要求的近似解的方法。