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Generalized functionals of Brownian motion and their applications : nonlinear functionals of fundamental stochastic processes /
This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener-Ito class including the generalized functionals of Hida as sp...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack :
World Scientific,
©2012.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1. Background material. 1.1. Introduction. 1.2. Wiener process and Wiener measure. 1.3. Stochastic differential equations in R[symbol]. 1.4. Stochastic differential equations in H. 1.5. Nonlinear filtering. 1.6. Elements of vector measures. 1.7. Some problems for exercise
- 2. Regular functionals of Brownian motion. 2.1. Introduction. 2.2. Functionals of scalar Brownian motion. 2.3. Functionals of vector Brownian motion. 2.4. Functionals of Gaussian random field (GRF). 2.5. Functionals of multidimensional Gaussian random fields. 2.6. Functionals of [symbol]-dimensional Brownian motion. 2.7. Fr-Br. motion and regular functionals thereof. 2.8. Levy process and regular functionals thereof. 2.9. Some problems for exercise
- 3. Generalized functionals of the first kind I. 3.1. Introduction. 3.2. Mild generalized functionals I. 3.3. Mild generalized functionals II. 3.4. Generalized functionals of GRF I. 3.5. Generalized functionals of GRF II. 3.6. Generalized functionals of [symbol]-dim. Brownian motion. 3.7. Generalized functionals of Fr. Brownian motion and Levy process. 3.8. Some problems for exercise
- 4. Functional analysis on {G, [symbol]} and their duals. 4.1. Introduction. 4.2. Compact and weakly compact sets. 4.3. Some optimization problems. 4.4. Applications to SDE. 4.5. Vector measures. 4.6. Application to nonlinear filtering. 4.7. Application to infinite dimensional systems. 4.8. Levy optimization problem. 4.9. Some problems for exercise
- 5. L[symbol]-based generalized functionals of white noise II. 5.1. Introduction. 5.2. Characteristic function of white noise. 5.3. Multiple Wiener-Ito integrals. 5.4. Generalized Hida-functionals. 5.5. Application to quantum mechanics. 5.6. Some problems for exercise
- 6. L[symbol]-based generalized functionals of white noise III. 6.1. Introduction. 6.2. Homogeneous functionals of degree n. 6.3. Nonhomogeneous functionals. 6.4. Weighted generalized functionals. 6.5. Some examples related to section 6.4. 6.6. Generalized functionals of random fields applied. 6.7. [symbol]valued vector measures with application. 6.8. Some problems for exercise
- 7. W[symbol]-based generalized functionals of white noise IV. 7.1. Introduction. 7.2. Homogeneous functionals. 7.3. Nonhomogeneous functionals. 7.4. Inductive and projective limits. 7.5. Abstract generalized functionals. 7.6. Vector measures with values from Wiener-Ito distributions. 7.7. Application to nonlinear filtering. 7.8. Application to stochastic Navier-Stokes equation. 7.9. Some problems for exercise
- 8. Some elements of Malliavin calculus. 8.1. Introduction. 8.2. Abstract Wiener space. 8.3. Malliavin derivative and integration by parts. 8.4. Operator [symbol] the adjoint of the operator D. 8.5. Ornstein-Uhlenbeck operator L. 8.6. Sobolev spaces on Wiener measure space [symbol] 8.7. Smoothness of probability measures. 8.8. Central limit theorem for Wiener-Ito Functionals. 8.9. Malliavin calculus for Fr-Brownian motion. 8.10. Some problems for exercise
- 9. Evolution equations on Fock spaces. 9.1. Introduction. 9.2. Malliavin operators on Fock spaces. 9.3. Evolution equations on abstract Fock spaces. 9.4. Evolution equations determined by coercive operators on Fock spaces. 9.5. An example. 9.6. Evolution equations on Wiener-Sobolev spaces. 9.7. Some examples for exercise.