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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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World Scientific,
©2012.
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| Zusammenfassung: | 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 special cases, among others. It presents a thorough and comprehensive treatment of the Wiener-Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems. Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated Riesz-Fischer theorem for separable Hilbert spaces and the space of Wiener-Ito functionals is drawn out, thus providing a clear insight into the subject. |
| Beschreibung: | 1 online resource (xiv, 299 pages) |
| Bibliographie: | Includes bibliographical references (pages 291-296) and index. |
| ISBN: | 9789814366373 9814366374 |
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| 100 | 1 | |a Ahmed, N. U. |q (Nasir Uddin) |1 https://id.oclc.org/worldcat/entity/E39PCjtkqXqpq77tGPRJGyqfbd |0 http://id.loc.gov/authorities/names/n81051848 | |
| 245 | 1 | 0 | |a Generalized functionals of Brownian motion and their applications : |b nonlinear functionals of fundamental stochastic processes / |c N U Ahmed. |
| 260 | |a Singapore ; |a Hackensack : |b World Scientific, |c ©2012. | ||
| 300 | |a 1 online resource (xiv, 299 pages) | ||
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| 504 | |a Includes bibliographical references (pages 291-296) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 520 | |a 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 special cases, among others. It presents a thorough and comprehensive treatment of the Wiener-Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems. Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated Riesz-Fischer theorem for separable Hilbert spaces and the space of Wiener-Ito functionals is drawn out, thus providing a clear insight into the subject. | ||
| 650 | 0 | |a Brownian motion processes. |0 http://id.loc.gov/authorities/subjects/sh85017265 | |
| 650 | 0 | |a Stochastic processes. |0 http://id.loc.gov/authorities/subjects/sh85128181 | |
| 650 | 2 | |a Stochastic Processes |0 https://id.nlm.nih.gov/mesh/D013269 | |
| 650 | 6 | |a Processus de mouvement brownien. | |
| 650 | 6 | |a Processus stochastiques. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Stochastic Processes. |2 bisacsh | |
| 650 | 7 | |a Brownian motion processes |2 fast | |
| 650 | 7 | |a Stochastic processes |2 fast | |
| 650 | 7 | |a Brownsche Bewegung |2 gnd |0 http://d-nb.info/gnd/4128328-4 | |
| 650 | 7 | |a Nichtlineares Funktional |2 gnd |0 http://d-nb.info/gnd/4604704-9 | |
| 650 | 7 | |a Stochastischer Prozess |2 gnd | |
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| author | Ahmed, N. U. (Nasir Uddin) |
| author_GND | http://id.loc.gov/authorities/names/n81051848 |
| author_facet | Ahmed, N. U. (Nasir Uddin) |
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| contents | 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. |
| ctrlnum | (OCoLC)777401301 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik |
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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.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">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 special cases, among others. It presents a thorough and comprehensive treatment of the Wiener-Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems. Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. 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| id | ZDB-4-EBA-ocn777401301 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:15Z |
| institution | BVB |
| isbn | 9789814366373 9814366374 |
| language | English |
| oclc_num | 777401301 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiv, 299 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
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| publisher | World Scientific, |
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| spelling | Ahmed, N. U. (Nasir Uddin) https://id.oclc.org/worldcat/entity/E39PCjtkqXqpq77tGPRJGyqfbd http://id.loc.gov/authorities/names/n81051848 Generalized functionals of Brownian motion and their applications : nonlinear functionals of fundamental stochastic processes / N U Ahmed. Singapore ; Hackensack : World Scientific, ©2012. 1 online resource (xiv, 299 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file rda Bibliography Includes bibliographical references (pages 291-296) and index. Print version record. 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. 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 special cases, among others. It presents a thorough and comprehensive treatment of the Wiener-Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems. Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated Riesz-Fischer theorem for separable Hilbert spaces and the space of Wiener-Ito functionals is drawn out, thus providing a clear insight into the subject. Brownian motion processes. http://id.loc.gov/authorities/subjects/sh85017265 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Processus de mouvement brownien. Processus stochastiques. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Brownian motion processes fast Stochastic processes fast Brownsche Bewegung gnd http://d-nb.info/gnd/4128328-4 Nichtlineares Funktional gnd http://d-nb.info/gnd/4604704-9 Stochastischer Prozess gnd has work: Generalized functionals of Brownian motion and their applications (Text) https://id.oclc.org/worldcat/entity/E39PCGBWqjmmrPXyWQjpQyx8P3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Ahmed, N.U. (Nasir Uddin). Generalized functionals of Brownian motion and their applications. Singapore ; Hackensack : World Scientific, ©2012 9789814366366 (OCoLC)740623008 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=426458 Volltext |
| spellingShingle | Ahmed, N. U. (Nasir Uddin) Generalized functionals of Brownian motion and their applications : nonlinear functionals of fundamental stochastic processes / 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. Brownian motion processes. http://id.loc.gov/authorities/subjects/sh85017265 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Processus de mouvement brownien. Processus stochastiques. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Brownian motion processes fast Stochastic processes fast Brownsche Bewegung gnd http://d-nb.info/gnd/4128328-4 Nichtlineares Funktional gnd http://d-nb.info/gnd/4604704-9 Stochastischer Prozess gnd |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85017265 http://id.loc.gov/authorities/subjects/sh85128181 https://id.nlm.nih.gov/mesh/D013269 http://d-nb.info/gnd/4128328-4 http://d-nb.info/gnd/4604704-9 |
| title | Generalized functionals of Brownian motion and their applications : nonlinear functionals of fundamental stochastic processes / |
| title_auth | Generalized functionals of Brownian motion and their applications : nonlinear functionals of fundamental stochastic processes / |
| title_exact_search | Generalized functionals of Brownian motion and their applications : nonlinear functionals of fundamental stochastic processes / |
| title_full | Generalized functionals of Brownian motion and their applications : nonlinear functionals of fundamental stochastic processes / N U Ahmed. |
| title_fullStr | Generalized functionals of Brownian motion and their applications : nonlinear functionals of fundamental stochastic processes / N U Ahmed. |
| title_full_unstemmed | Generalized functionals of Brownian motion and their applications : nonlinear functionals of fundamental stochastic processes / N U Ahmed. |
| title_short | Generalized functionals of Brownian motion and their applications : |
| title_sort | generalized functionals of brownian motion and their applications nonlinear functionals of fundamental stochastic processes |
| title_sub | nonlinear functionals of fundamental stochastic processes / |
| topic | Brownian motion processes. http://id.loc.gov/authorities/subjects/sh85017265 Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Processus de mouvement brownien. Processus stochastiques. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Brownian motion processes fast Stochastic processes fast Brownsche Bewegung gnd http://d-nb.info/gnd/4128328-4 Nichtlineares Funktional gnd http://d-nb.info/gnd/4604704-9 Stochastischer Prozess gnd |
| topic_facet | Brownian motion processes. Stochastic processes. Stochastic Processes Processus de mouvement brownien. Processus stochastiques. MATHEMATICS Probability & Statistics Stochastic Processes. Brownian motion processes Stochastic processes Brownsche Bewegung Nichtlineares Funktional Stochastischer Prozess |
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