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Quantitative Analysis
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
1. Calculational Linear Algebra.
2. Wavelet Analysis.
A. Elementary definitions of wavelet analysis.
B. Haar functions.
C. Multiresolution analysis.
D. Orthonormal wavelet bases.
E. Discrete wavelet transform.
F. Construction of MRA from scaling filter or auxiliary function.
G. Consequences and conditions for vanishing moments of wavelets.
H. Existence of smooth compactly supported wavelets. Daubechies polynomials.
I. Semi-orthogonal wavelet bases.
a. Biorthogonal bases.
b. Riesz bases.
c. Generalized multiresolution analysis.
d. Dual generalized multiresolution analysis.
e. Dual wavelets.
f. Orthogonality across scales.
g. Biorthogonal QMF conditions.
h. Vanishing moments for biorthogonal wavelets.
i. Compactly supported smooth biorthogonal wavelets.
j. Spline functions.
k. Calculation of spline biorthogonal wavelets.
l. Symmetric biorthogonal wavelets.
J. Construction of (G)MRA and wavelets on an interval.
3. Finite element method.
4. Construction of approximation spaces.
5. Time discretization.
6. Variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Semi-orthogonal wavelet bases.


he procedure of the proposition ( Existence of smooth compactly supported wavelets ) leaves very little control over the resulting wavelets. In particular, the wavelets are not symmetrical and the smoothness of wavelets grows slowly with complexity (parameter $n$ ) of the procedure. Most of the freedom is lost due to the requirement of orthogonality across location index. In this section we discuss a procedure that drops orthogonality across location index but preserves most analytical properties.




a. Biorthogonal bases.
b. Riesz bases.
c. Generalized multiresolution analysis.
d. Dual generalized multiresolution analysis.
e. Dual wavelets.
f. Orthogonality across scales.
g. Biorthogonal QMF conditions.
h. Vanishing moments for biorthogonal wavelets.
i. Compactly supported smooth biorthogonal wavelets.
j. Spline functions.
k. Calculation of spline biorthogonal wavelets.
l. Symmetric biorthogonal wavelets.

Notation. Index. Contents.


















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