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The Resource Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction, Horst Osswald

Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction, Horst Osswald

Label
Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction
Title
Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion
Title remainder
an introduction
Statement of responsibility
Horst Osswald
Creator
Subject
Language
eng
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"--
Member of
Assigning source
Provided by publisher
Cataloging source
DLC
http://library.link/vocab/creatorName
Osswald, Horst
Dewey number
519.2/3
Index
index present
LC call number
QA274
LC item number
.O87 2012
Literary form
non fiction
Nature of contents
bibliography
Series statement
Cambridge tracts in mathematics
Series volume
191
http://library.link/vocab/subjectName
  • Malliavin calculus
  • Lévy processes
  • Brownian motion processes
  • MATHEMATICS / Probability & Statistics / General
Label
Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction, Horst Osswald
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
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
Control code
756578576
Extent
pages cm.
Isbn
9781107016149
Lccn
2011051230
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
System control number
(OCoLC)756578576
Label
Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : an introduction, Horst Osswald
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
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
Control code
756578576
Extent
pages cm.
Isbn
9781107016149
Lccn
2011051230
Media category
unmediated
Media MARC source
rdamedia.
Media type code
  • n
System control number
(OCoLC)756578576

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