National Science Library of Georgia

Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion : (Record no. 517847)

MARC details
000 -LEADER
fixed length control field 03645nam a22003858i 4500
001 - CONTROL NUMBER
control field CR9781139060110
003 - CONTROL NUMBER IDENTIFIER
control field UkCbUP
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20200124160233.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION
fixed length control field m|||||o||d||||||||
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr||||||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 110406s2012||||enk o ||1 0|eng|d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781139060110 (ebook)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Cancelled/invalid ISBN 9781107016149 (hardback)
040 ## - CATALOGING SOURCE
Original cataloging agency UkCbUP
Language of cataloging eng
Description conventions rda
Transcribing agency UkCbUP
050 00 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA274
Item number .O87 2012
082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 519.2/3
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Osswald, Horst,
Relator term author.
245 10 - TITLE STATEMENT
Title Malliavin calculus for Lévy processes and infinite-dimensional Brownian motion :
Remainder of title an introduction /
Statement of responsibility, etc Horst Osswald.
246 3# - VARYING FORM OF TITLE
Title proper/short title Malliavin Calculus for Lévy Processes & Infinite-Dimensional Brownian Motion
264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R)
Place of production, publication, distribution, manufacture (R) Cambridge :
Name of producer, publisher, distributor, manufacturer (R) Cambridge University Press,
Date of production, publication, distribution, manufacture, or copyright notice 2012.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (xix, 407 pages) :
Other physical details digital, PDF file(s).
336 ## - Content Type (R)
Content type term (R) text
Content type code (R) txt
Source (NR) rdacontent
337 ## - Media Type (R)
Media type term (R) computer
Media type code (R) c
Source (NR) rdamedia
338 ## - Carrier Type (R)
Carrier type term (R) online resource
Carrier type code (R) cr
Source (NR) rdacarrier
490 1# - SERIES STATEMENT
სერიის ცნობა Cambridge tracts in mathematics ;
Volume number/sequential designation 191
500 ## - GENERAL NOTE
General note Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note 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 ## - SUMMARY, ETC.
Summary, etc 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 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Malliavin calculus.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Lévy processes.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Brownian motion processes.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Print version:
International Standard Book Number 9781107016149
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Cambridge tracts in mathematics ;
Volume number/sequential designation 191.
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://doi.org/10.1017/CBO9781139060110">https://doi.org/10.1017/CBO9781139060110</a>

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