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 analysis...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2012
|
| Series: | Cambridge tracts in mathematics
191 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | 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 |
| Physical Description: | 1 Online-Ressource (xix, 407 Seiten) |
| ISBN: | 9781139060110 |
| DOI: | 10.1017/CBO9781139060110 |
Staff View
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| 505 | 8 | |a Martingales -- Fourier and Laplace transformations -- Abstract Wiener-Fréchet spaces -- Two concepts of no-anticipation in time -- Malliavin calculus on the space of real sequences -- Introduction to poly-saturated models of mathematics -- Extension of the real numbers -- Topology -- Measure and integration on Loeb spaces -- From finite- to infinite-dimensional Brownian motion -- The Itô integral for infinite-dimensional Brownian motion -- Multiple integrals -- Infinite-dimensional Ornstein-Uhlenbeck processes -- Lindstrøm's construction of standard Lévy processes from discrete ones -- Stochastic integration for Lévy processes -- Chaos decomposition (for infinite-dimensional Brownian motion) -- The Malliavin derivative -- The Skorohod integral -- The interplay between derivative and integral -- Skorohod integral processes -- Girsanov transformations -- 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) -- Poly-saturated models -- The existence of poly-saturated models | |
| 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 | ||
| 650 | 4 | |a Malliavin calculus | |
| 650 | 4 | |a Lévy processes | |
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Record in the Search Index
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| any_adam_object | |
| author | Osswald, Horst 1941- |
| author_GND | (DE-588)1023531968 |
| author_facet | Osswald, Horst 1941- |
| author_role | aut |
| author_sort | Osswald, Horst 1941- |
| author_variant | h o ho |
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| bvnumber | BV043941700 |
| classification_rvk | SK 820 |
| collection | ZDB-20-CBO |
| contents | Martingales -- Fourier and Laplace transformations -- Abstract Wiener-Fréchet spaces -- Two concepts of no-anticipation in time -- Malliavin calculus on the space of real sequences -- Introduction to poly-saturated models of mathematics -- Extension of the real numbers -- Topology -- Measure and integration on Loeb spaces -- From finite- to infinite-dimensional Brownian motion -- The Itô integral for infinite-dimensional Brownian motion -- Multiple integrals -- Infinite-dimensional Ornstein-Uhlenbeck processes -- Lindstrøm's construction of standard Lévy processes from discrete ones -- Stochastic integration for Lévy processes -- Chaos decomposition (for infinite-dimensional Brownian motion) -- The Malliavin derivative -- The Skorohod integral -- The interplay between derivative and integral -- Skorohod integral processes -- Girsanov transformations -- 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) -- Poly-saturated models -- The existence of poly-saturated models |
| ctrlnum | (ZDB-20-CBO)CR9781139060110 (OCoLC)852511433 (DE-599)BVBBV043941700 |
| dewey-full | 519.2/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 |
| dewey-search | 519.2/3 |
| dewey-sort | 3519.2 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139060110 |
| format | Electronic eBook |
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| id | DE-604.BV043941700 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9781139060110 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350670 |
| oclc_num | 852511433 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xix, 407 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 2012 |
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| publisher | Cambridge University Press |
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| spelling | Osswald, Horst 1941- Verfasser (DE-588)1023531968 aut Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion an introduction Horst Osswald Malliavin Calculus for Lévy Processes & Infinite-Dimensional Brownian Motion Cambridge Cambridge University Press 2012 1 Online-Ressource (xix, 407 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 191 Martingales -- Fourier and Laplace transformations -- Abstract Wiener-Fréchet spaces -- Two concepts of no-anticipation in time -- Malliavin calculus on the space of real sequences -- Introduction to poly-saturated models of mathematics -- Extension of the real numbers -- Topology -- Measure and integration on Loeb spaces -- From finite- to infinite-dimensional Brownian motion -- The Itô integral for infinite-dimensional Brownian motion -- Multiple integrals -- Infinite-dimensional Ornstein-Uhlenbeck processes -- Lindstrøm's construction of standard Lévy processes from discrete ones -- Stochastic integration for Lévy processes -- Chaos decomposition (for infinite-dimensional Brownian motion) -- The Malliavin derivative -- The Skorohod integral -- The interplay between derivative and integral -- Skorohod integral processes -- Girsanov transformations -- 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) -- Poly-saturated models -- The existence of poly-saturated models 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 Malliavin calculus Lévy processes Brownian motion processes Malliavin-Kalkül (DE-588)4242584-0 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Lévy-Prozess (DE-588)4463623-4 gnd rswk-swf Lévy-Prozess (DE-588)4463623-4 s Brownsche Bewegung (DE-588)4128328-4 s Malliavin-Kalkül (DE-588)4242584-0 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-107-01614-9 https://doi.org/10.1017/CBO9781139060110 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Osswald, Horst 1941- Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion an introduction Martingales -- Fourier and Laplace transformations -- Abstract Wiener-Fréchet spaces -- Two concepts of no-anticipation in time -- Malliavin calculus on the space of real sequences -- Introduction to poly-saturated models of mathematics -- Extension of the real numbers -- Topology -- Measure and integration on Loeb spaces -- From finite- to infinite-dimensional Brownian motion -- The Itô integral for infinite-dimensional Brownian motion -- Multiple integrals -- Infinite-dimensional Ornstein-Uhlenbeck processes -- Lindstrøm's construction of standard Lévy processes from discrete ones -- Stochastic integration for Lévy processes -- Chaos decomposition (for infinite-dimensional Brownian motion) -- The Malliavin derivative -- The Skorohod integral -- The interplay between derivative and integral -- Skorohod integral processes -- Girsanov transformations -- 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) -- Poly-saturated models -- The existence of poly-saturated models Malliavin calculus Lévy processes Brownian motion processes Malliavin-Kalkül (DE-588)4242584-0 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Lévy-Prozess (DE-588)4463623-4 gnd |
| subject_GND | (DE-588)4242584-0 (DE-588)4128328-4 (DE-588)4463623-4 |
| title | Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion an introduction |
| title_alt | Malliavin Calculus for Lévy Processes & Infinite-Dimensional Brownian Motion |
| 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 Lévy processes Brownian motion processes Malliavin-Kalkül (DE-588)4242584-0 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Lévy-Prozess (DE-588)4463623-4 gnd |
| topic_facet | Malliavin calculus Lévy processes Brownian motion processes Malliavin-Kalkül Brownsche Bewegung Lévy-Prozess |
| url | https://doi.org/10.1017/CBO9781139060110 |
| work_keys_str_mv | AT osswaldhorst malliavincalculusforlevyprocessesandinfinitedimensionalbrownianmotionanintroduction AT osswaldhorst malliavincalculusforlevyprocessesinfinitedimensionalbrownianmotion |