Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion :: an introduction /
"Assuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard an...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
©2012.
|
| Schriftenreihe: | Cambridge tracts in mathematics ;
191. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "Assuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard analysis, which allows infinite-dimensional problems to be treated as finite-dimensional. The result is an intuitive, indeed enjoyable, development of both Malliavin calculus and nonstandard analysis. The main aspects of stochastic analysis and Malliavin calculus are incorporated into this simplifying framework. Topics covered include Brownian motion, Ornstein-Uhlenbeck processes both with values in abstract Wiener spaces, Lévy processes, multiple stochastic integrals, chaos decomposition, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes and Girsanov transformations. The careful exposition, which is neither too abstract nor too theoretical, makes this book accessible to graduate students, as well as to researchers interested in the techniques"-- |
| Beschreibung: | 1 online resource |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781139233842 113923384X 1139230859 9781139230858 1139232304 9781139232302 9781139060110 1139060112 |
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| 520 | |a "Assuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard analysis, which allows infinite-dimensional problems to be treated as finite-dimensional. The result is an intuitive, indeed enjoyable, development of both Malliavin calculus and nonstandard analysis. The main aspects of stochastic analysis and Malliavin calculus are incorporated into this simplifying framework. Topics covered include Brownian motion, Ornstein-Uhlenbeck processes both with values in abstract Wiener spaces, Lévy processes, multiple stochastic integrals, chaos decomposition, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes and Girsanov transformations. The careful exposition, which is neither too abstract nor too theoretical, makes this book accessible to graduate students, as well as to researchers interested in the techniques"-- |c Provided by publisher | ||
| 505 | 0 | |a 1. Preface -- 2. Martingales -- 3. Fourier and Laplace transformations -- 4. Abstract Wiener-Fréchet spaces -- 5. Two concepts of no-anticipation in time -- 6. Malliavin calculus on the space of real sequences -- 7. Introduction to poly-saturated models of mathematics -- 8. Extension of the real numbers -- 9. Topology -- 10. Measure and integration on Loeb spaces -- 11. From finite- to infinite-dimensional Brownian motion -- 12. The Itô integral for infinite-dimensional Brownian motion -- 13. Multiple integrals -- 14. Infinite-dimensional Ornstein-Uhlenbeck processes -- 15. Lindstrøm's construction of standard Lévy processes from discrete ones -- 16. Stochastic integration for Lévy processes -- 17. Chaos decomposition (for infinite-dimensional Brownian motion) -- 18. The Malliavin derivative -- 19. The Skorohod integral -- 20. The interplay between derivative and integral -- 21. Skorohod integral processes -- 22. Girsanov transformations -- 23. Malliavin calculus for Lévy processes (Chaos, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes, Smooth representations, a communication rule for derivative and limit, product-, chainrule, Girsanov transformations) -- 24. Poly-saturated models -- 25. The existence of poly-saturated models -- References -- Index. | |
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| 650 | 0 | |a Brownian motion processes. |0 http://id.loc.gov/authorities/subjects/sh85017265 | |
| 650 | 6 | |a Calcul de Malliavin. | |
| 650 | 6 | |a Lévy, Processus de. | |
| 650 | 6 | |a Processus de mouvement brownien. | |
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| contents | 1. Preface -- 2. Martingales -- 3. Fourier and Laplace transformations -- 4. Abstract Wiener-Fréchet spaces -- 5. Two concepts of no-anticipation in time -- 6. Malliavin calculus on the space of real sequences -- 7. Introduction to poly-saturated models of mathematics -- 8. Extension of the real numbers -- 9. Topology -- 10. Measure and integration on Loeb spaces -- 11. From finite- to infinite-dimensional Brownian motion -- 12. The Itô integral for infinite-dimensional Brownian motion -- 13. Multiple integrals -- 14. Infinite-dimensional Ornstein-Uhlenbeck processes -- 15. Lindstrøm's construction of standard Lévy processes from discrete ones -- 16. Stochastic integration for Lévy processes -- 17. Chaos decomposition (for infinite-dimensional Brownian motion) -- 18. The Malliavin derivative -- 19. The Skorohod integral -- 20. The interplay between derivative and integral -- 21. Skorohod integral processes -- 22. Girsanov transformations -- 23. Malliavin calculus for Lévy processes (Chaos, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes, Smooth representations, a communication rule for derivative and limit, product-, chainrule, Girsanov transformations) -- 24. Poly-saturated models -- 25. The existence of poly-saturated models -- References -- Index. |
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| indexdate | 2024-11-27T13:18:18Z |
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| series | Cambridge tracts in mathematics ; |
| series2 | Cambridge tracts in mathematics ; |
| spelling | Osswald, Horst. http://id.loc.gov/authorities/names/n2001016049 Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction / Horst Osswald. Cambridge : Cambridge University Press, ©2012. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge tracts in mathematics ; 191 Includes bibliographical references and index. "Assuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard analysis, which allows infinite-dimensional problems to be treated as finite-dimensional. The result is an intuitive, indeed enjoyable, development of both Malliavin calculus and nonstandard analysis. The main aspects of stochastic analysis and Malliavin calculus are incorporated into this simplifying framework. Topics covered include Brownian motion, Ornstein-Uhlenbeck processes both with values in abstract Wiener spaces, Lévy processes, multiple stochastic integrals, chaos decomposition, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes and Girsanov transformations. The careful exposition, which is neither too abstract nor too theoretical, makes this book accessible to graduate students, as well as to researchers interested in the techniques"-- Provided by publisher 1. Preface -- 2. Martingales -- 3. Fourier and Laplace transformations -- 4. Abstract Wiener-Fréchet spaces -- 5. Two concepts of no-anticipation in time -- 6. Malliavin calculus on the space of real sequences -- 7. Introduction to poly-saturated models of mathematics -- 8. Extension of the real numbers -- 9. Topology -- 10. Measure and integration on Loeb spaces -- 11. From finite- to infinite-dimensional Brownian motion -- 12. The Itô integral for infinite-dimensional Brownian motion -- 13. Multiple integrals -- 14. Infinite-dimensional Ornstein-Uhlenbeck processes -- 15. Lindstrøm's construction of standard Lévy processes from discrete ones -- 16. Stochastic integration for Lévy processes -- 17. Chaos decomposition (for infinite-dimensional Brownian motion) -- 18. The Malliavin derivative -- 19. The Skorohod integral -- 20. The interplay between derivative and integral -- 21. Skorohod integral processes -- 22. Girsanov transformations -- 23. Malliavin calculus for Lévy processes (Chaos, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes, Smooth representations, a communication rule for derivative and limit, product-, chainrule, Girsanov transformations) -- 24. Poly-saturated models -- 25. The existence of poly-saturated models -- References -- Index. Print version record. Malliavin calculus. http://id.loc.gov/authorities/subjects/sh91004306 Lévy processes. http://id.loc.gov/authorities/subjects/sh95010454 Brownian motion processes. http://id.loc.gov/authorities/subjects/sh85017265 Calcul de Malliavin. Lévy, Processus de. Processus de mouvement brownien. MATHEMATICS Probability & Statistics General. bisacsh MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Probabilidades embne Procesos estocásticos embne Brownian motion processes fast Lévy processes fast Malliavin calculus fast has work: Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion (Text) https://id.oclc.org/worldcat/entity/E39PCGJXKpJmGChcDPkHccHJwC https://id.oclc.org/worldcat/ontology/hasWork Print version: Osswald, Horst. Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion. Cambridge : Cambridge University Press, 2012 9781107016149 (DLC) 2011051230 (OCoLC)756578576 Cambridge tracts in mathematics ; 191. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=435275 Volltext |
| spellingShingle | Osswald, Horst Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction / Cambridge tracts in mathematics ; 1. Preface -- 2. Martingales -- 3. Fourier and Laplace transformations -- 4. Abstract Wiener-Fréchet spaces -- 5. Two concepts of no-anticipation in time -- 6. Malliavin calculus on the space of real sequences -- 7. Introduction to poly-saturated models of mathematics -- 8. Extension of the real numbers -- 9. Topology -- 10. Measure and integration on Loeb spaces -- 11. From finite- to infinite-dimensional Brownian motion -- 12. The Itô integral for infinite-dimensional Brownian motion -- 13. Multiple integrals -- 14. Infinite-dimensional Ornstein-Uhlenbeck processes -- 15. Lindstrøm's construction of standard Lévy processes from discrete ones -- 16. Stochastic integration for Lévy processes -- 17. Chaos decomposition (for infinite-dimensional Brownian motion) -- 18. The Malliavin derivative -- 19. The Skorohod integral -- 20. The interplay between derivative and integral -- 21. Skorohod integral processes -- 22. Girsanov transformations -- 23. Malliavin calculus for Lévy processes (Chaos, Malliavin derivative, Clark-Ocone formula, Skorohod integral processes, Smooth representations, a communication rule for derivative and limit, product-, chainrule, Girsanov transformations) -- 24. Poly-saturated models -- 25. The existence of poly-saturated models -- References -- Index. Malliavin calculus. http://id.loc.gov/authorities/subjects/sh91004306 Lévy processes. http://id.loc.gov/authorities/subjects/sh95010454 Brownian motion processes. http://id.loc.gov/authorities/subjects/sh85017265 Calcul de Malliavin. Lévy, Processus de. Processus de mouvement brownien. MATHEMATICS Probability & Statistics General. bisacsh MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Probabilidades embne Procesos estocásticos embne Brownian motion processes fast Lévy processes fast Malliavin calculus fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh91004306 http://id.loc.gov/authorities/subjects/sh95010454 http://id.loc.gov/authorities/subjects/sh85017265 |
| title | Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction / |
| title_auth | Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction / |
| title_exact_search | Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction / |
| title_full | Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction / Horst Osswald. |
| title_fullStr | Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction / Horst Osswald. |
| title_full_unstemmed | Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction / Horst Osswald. |
| title_short | Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : |
| title_sort | malliavin calculus for levy processes and infinite dimensional brownian motion an introduction |
| title_sub | an introduction / |
| topic | Malliavin calculus. http://id.loc.gov/authorities/subjects/sh91004306 Lévy processes. http://id.loc.gov/authorities/subjects/sh95010454 Brownian motion processes. http://id.loc.gov/authorities/subjects/sh85017265 Calcul de Malliavin. Lévy, Processus de. Processus de mouvement brownien. MATHEMATICS Probability & Statistics General. bisacsh MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Probabilidades embne Procesos estocásticos embne Brownian motion processes fast Lévy processes fast Malliavin calculus fast |
| topic_facet | Malliavin calculus. Lévy processes. Brownian motion processes. Calcul de Malliavin. Lévy, Processus de. Processus de mouvement brownien. MATHEMATICS Probability & Statistics General. MATHEMATICS Probability & Statistics Stochastic Processes. Probabilidades Procesos estocásticos Brownian motion processes Lévy processes Malliavin calculus |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=435275 |
| work_keys_str_mv | AT osswaldhorst malliavincalculusforlevyprocessesandinfinitedimensionalbrownianmotionanintroduction |