美式看跌期权定价中的小波方法

本文采用有限差分格式和 Daubechies正交小波 ,提出了一种求解 Black- Scholes方程数值解新算法 .为美式看跌期定价提供了一条新的途径 .利用小波基的自适应性和消失矩特性 ,使偏微分算子矩阵和小波级数稀疏化 ,大大减少了计算量 .     

Besov 空间上的算子插值定理

本文研究了算子的插值问题.利用Riesz-Thorin定理的证明方法,并运用Daubechies小波得到了Besov空间上的线性算子的插值定理.     

用小波限制紧算子逼近奇异积分算子的速度

根据Beylin-Coifman-Rokhlin和Yang的观点，用合适的小波基可以刻画性地研究C.Z算子或拟微分算子，这样就可以用小波来计算算子，比如可以从奇异积分算子的B-C-R算法刻画出发，用小波限制紧算子进行逼近，本文旨在计算作为原算子与逼近算子的差的误差算子的H1到L1的连续性范数的最佳衰减速度和在Lp上的连续性范数的衰减速度的范围。     

结合小波理论讲授泛函分析课程

对泛函分析课程教学中的一些应用问题进行了探讨,阐述了泛函分析在小波理论中的应用,重点说明希尔伯特空间的正交性、伴随算子、投影算子以及依范数收敛、弱*收敛在小波理论中的体现.     

小波分析中的一个非线性算子

在这篇文章里,我们以算子的观点考虑了小波的构造问题．结果,我们得到了小波分析中一个非线性算子并调查了这个非线性算子的一些性质．     

求解非线性Black-Scholes模型的自适应小波精细积分法

针对非线性Black-Scholes方程,基于quasi-Shannon小波函数给出了一种求解非线性偏微分方程的自适应多尺度小波精细积分法.该方法首先利用插值小波理论构造了用于逼近连续函数的多尺度小波插值算子,利用该算子可以将非线性Black-Scholes方程自适应离散为非线性常微分方程组;然后将用于求解常微分方程组的精细积分法和小波变换的动态过程相结合,并利用非线性处理技术(如同伦分析技术)可有效求解非线性Black-Scholes方程.数值结果表明了该方法在数值精度和计算效率方面的优越性.     

VG扭曲算子在期权定价中的应用

利用概率变换思路,基于VG分布提出了VG扭曲算子.在VG模型中,证明了按VG扭曲算子得到的期权价格和在均值修正鞅测度下的期权价格一致.数值计算结果表明,按VG扭曲算子得到的期权价格比较准确.     

再生核空间中的微分算子样条小波

0　引　　言r次多项式样条小波是从一个满足特殊的广义微分方程Dr+1φ(x)=δ(x)(D是广义微分子算子)的解φ(x)=xr+r!出发来构造的,文献[1]根据这一思想给出非多项式的H1(R)空间中微分算子样条小波分析的构造方法,本文基于这一思路来讨论W2(R)空间中的微分算子样条小波理论.在W2(R)空间中讨论非多项式形式的微分算子样条小波分析理论,这是多项式小波理论自然深入的发展.本文首先给出W2(R)空间中小波分析定义,然后给出小波函数在时、频域上的表达式,最后利用W2(R)空间中的若干特殊性质,给出小波的投影表达式.并证明了投影逼近函数uj(X)…     

一种结合小波模极大值法和Canny算子的目标提取方法

针对基于小波变换的目标提取中忽略低频子图像的一些重要信息的问题.提出了一种基于小波变换的模极大值法和Canny算子的目标提取方法.在小波域中,通过求解局部小波系数模型的极大值点提取(检测)高频边缘,利用Canny算子提取(检测)低频边缘.然后根据融合规则对两个子图像边缘进行融合.实验结果表明,该方法不仅能有效地增强图像边缘,而且能准确地定位图像边缘.     

框架提升的两种方案

该文给出了框架提升的两种方案,这两种方案能够使作者对已有的二进小波框架或滤波器进行修正从而构造出新的小波框架.特别地,这两种方案能够使作者从分段线性的样条紧框架的张量积出发设计出不可分框架,新的框架能起到π/4的整数倍方向上的加权平均算子、Sobel算子和Laplacian算子的作用.     

Wavelet approximations of a collision operator in kinetic theory

This Note is devoted to the derivation of conservative and entropic fast wavelet approximations for the isotropic Fokker–Planck–Landau collision operator arising in the modeling of charged particles in plasma physics. The present approach combines the advantages of both the finite difference schemes (conservation and entropy) and the spectral methods (accuracy) which are developed in the literature. Furthermore, the wavelet approach provides a fast algorithm for the evaluation of such a collision operator. The present work is a first step to the development of wavelet approximations to more complex collision operators in kinetic theory. To cite this article: X. Antoine, M. Lemou, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Band-Limited Wavelets

Using the harmonic method,we get a class of more general band-limited wavelet,which was got by complicate operator interpolation method before.Our result is alittle better than the result by operator interpolation method.The fast band-limitedwavelet transform shall be given in another paper.     

Wavelets on manifolds: An optimized construction

A key ingredient of the construction of biorthogonal wavelet bases for Sobolev spaces on manifolds, which is based on topological isomorphisms is the Hestenes extension operator. Here we firstly investigate whether this particular extension operator can be replaced by another extension operator. Our main theoretical result states that an important class of extension operators based on interpolating boundary values cannot be used in the construction setting required by Dahmen and Schneider. In the second part of this paper, we investigate and optimize the Hestenes extension operator. The results of the optimization process allow us to implement the construction of biorthogonal wavelets from Dahmen and Schneider. As an example, we illustrate a wavelet basis on the 2-sphere.

     

Efficient application of nonlinear stationary operators in adaptive wavelet methods—the isotropic case

This paper deals with the efficient application of nonlinear operators in wavelet coordinates using a representation based on local polynomials. In the framework of adaptive wavelet methods for solving, e.g., PDEs or eigenvalue problems, one has to apply the operator to a vector on a target wavelet index set. The central task is to apply the operator as fast as possible in order to obtain an efficient overall scheme. This work presents a new approach of dealing with this problem. The basic ideas together with an implementation for a specific PDE on an L-shaped domain were presented firstly in [38]. Considering the approximation of a function based on wavelets consisting of piecewise polynomials, e.g., spline wavelets, one can represent each wavelet using local polynomials on cells of the underlying domain. Because of the multilevel structure of the wavelet spaces, the generated polynomial usually consists of many overlapping pieces living on different spatial levels. Since nonlinear operators, by definition, cannot generally be applied to a linear decomposition exactly, a locally unique representation is sought. The application of the operator to these polynomials now has a simple structure due to the locality of the polynomials and many operators can be applied exactly to the local polynomials. From these results, the values of the target wavelet index set can be reconstructed. It is shown that all these steps can be applied in optimal linear complexity. The purpose of the presented paper is to provide a self-consistent development of this operator application independent of the particular PDE, operator, underlying domain, types of wavelets, or space dimension, thereby extending and modifying the previous ideas from [38].     

连续小波变换及小波框架算子的一些性质

以泛函分析的观点来考察连续小波变换及小波框架算子，得到了它们的一些性质，并给出了严格证明，弥补了有关献中的不足。     

多重向量值正交小波包

本文引入多重向量值小波包的概念,提供一类多重向量值正交小波包的构造方法,并运用积分变换和算子理论,讨论了多重向量值正交小波包的性质．利用多重向量值正交小波包,构造了空间L2(R,Cs×s)的新的正交基．     

Mexican hat wavelet transform of distributions

Theory of Weierstrass transform is exploited to derive many interesting new properties of the Mexican hat wavelet transform. A real inversion formula in the differential operator form for the Mexican hat wavelet transform is established. Mexican hat wavelet transform of distributions is defined and its properties are studied. An approximation property of the distributional wavelet transform is investigated which is supported by a nice example.     

A wavelet-based nested iteration–inexact conjugate gradient algorithm for adaptively solving elliptic PDEs

In Cohen et al. (Math Comput 70:27–75, 2001), a new paradigm for the adaptive solution of linear elliptic partial differential equations (PDEs) was proposed, based on wavelet discretizations. Starting from a well-conditioned representation of the linear operator equation in infinite wavelet coordinates, one performs perturbed gradient iterations involving approximate matrix–vector multiplications of finite portions of the operator. In a bootstrap-type fashion, increasingly smaller tolerances guarantee convergence of the adaptive method. In addition, coarsening performed on the iterates allow one to prove asymptotically optimal complexity results when compared to the wavelet best N-term approximation. In the present paper, we study adaptive wavelet schemes for symmetric operators employing inexact conjugate gradient routines. Inspired by fast schemes on uniform grids, we incorporate coarsening and the adaptive application of the elliptic operator into a nested iteration algorithm. Our numerical results demonstrate that the runtime of the algorithm is linear in the number of unknowns and substantial savings in memory can be achieved in two and three space dimensions.