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The Resource Introduction to Stochastic Integration, by K.L. Chung, R.J. Williams, (electronic resource)

Introduction to Stochastic Integration, by K.L. Chung, R.J. Williams, (electronic resource)

Creator
Author
Contributor
Summary
A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability. Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then Itô's change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman--Kac functional and theSchrödinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed. New to the second edition are a discussion of the Cameron--Martin--Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use. This book will be a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis. The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory. --Journal of the American Statistical Association An attractive text...written in [a] lean and precise style...eminently readable. Especially pleasant are the care and attention devoted to details... A very fine book. --Mathematical Reviews
Language
eng
Work
Publication
Edition
Second edition 2014.
Extent
XVII, 276 pages 10 illustrations
Contents
  • 1 Preliminaries
  • 2 Definition of the Stochastic Integral
  • 3 Extension of the Predictable Integrands
  • 4 Quadratic Variation Process
  • 5 The Ito Formula
  • 6 Applications of the Ito Formula
  • 7 Local Time and Tanaka's Formula
  • 8 Reflected Brownian Motions
  • 9 Generalization Ito Formula, Change of Time and Measure
  • 10 Stochastic Differential Equations
  • References
  • Index
Isbn
9781461495871
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4614-9587-1
Instance
Label
Introduction to Stochastic Integration
Title
Introduction to Stochastic Integration
Statement of responsibility
by K.L. Chung, R.J. Williams
Creator
Contributor
Author
Subject
Language
eng
Summary
A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability. Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then Itô's change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman--Kac functional and theSchrödinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed. New to the second edition are a discussion of the Cameron--Martin--Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use. This book will be a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis. The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory. --Journal of the American Statistical Association An attractive text...written in [a] lean and precise style...eminently readable. Especially pleasant are the care and attention devoted to details... A very fine book. --Mathematical Reviews
Member of
Cataloging source
IT-FiEUI
http://library.link/vocab/creatorDate
1917-2009
http://library.link/vocab/creatorName
Chung, Kai Lai
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorDate
1955-
http://library.link/vocab/relatedWorkOrContributorName
  • Williams, R. J.
  • SpringerLink (Online service)
Series statement
  • Modern Birkhäuser Classics,
  • Springer eBooks
http://library.link/vocab/subjectName
  • Mathematics
  • Distribution (Probability theory)
Label
Introduction to Stochastic Integration, by K.L. Chung, R.J. Williams, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4614-9587-1
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
1 Preliminaries -- 2 Definition of the Stochastic Integral -- 3 Extension of the Predictable Integrands -- 4 Quadratic Variation Process -- 5 The Ito Formula -- 6 Applications of the Ito Formula -- 7 Local Time and Tanaka's Formula -- 8 Reflected Brownian Motions -- 9 Generalization Ito Formula, Change of Time and Measure -- 10 Stochastic Differential Equations -- References -- Index
Control code
978-1-4614-9587-1
Dimensions
unknown
Edition
Second edition 2014.
Extent
XVII, 276 pages 10 illustrations
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781461495871
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4614-9587-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1058472822
Label
Introduction to Stochastic Integration, by K.L. Chung, R.J. Williams, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4614-9587-1
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
1 Preliminaries -- 2 Definition of the Stochastic Integral -- 3 Extension of the Predictable Integrands -- 4 Quadratic Variation Process -- 5 The Ito Formula -- 6 Applications of the Ito Formula -- 7 Local Time and Tanaka's Formula -- 8 Reflected Brownian Motions -- 9 Generalization Ito Formula, Change of Time and Measure -- 10 Stochastic Differential Equations -- References -- Index
Control code
978-1-4614-9587-1
Dimensions
unknown
Edition
Second edition 2014.
Extent
XVII, 276 pages 10 illustrations
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781461495871
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4614-9587-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1058472822

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