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The Resource Introduction to stochastic integration, Hui-Hsiung Kuo

Introduction to stochastic integration, Hui-Hsiung Kuo

Creator
Summary
The theory of stochastic integration, also called the Ito calculus, has a large spectrum of applications in virtually every scientific area involving random functions, but it can be a very difficult subject for people without much mathematical background. The Ito calculus was originally motivated by the construction of Markov diffusion processes from infinitesimal generators. Previously, the construction of such processes required several steps, whereas Ito constructed these diffusion processes directly in a single step as the solutions of stochastic integral equations associated with the infinitesimal generators. Moreover, the properties of these diffusion processes can be derived from the stochastic integral equations and the Ito formula. This introductory textbook on stochastic integration provides a concise introduction to the Ito calculus, and covers the following topics: @* Constructions of Brownian motion; @* Stochastic integrals for Brownian motion and martingales; @* The Ito formula; @* Multiple Wiener-Ito integrals; @* Stochastic differential equations; @* Applications to finance, filtering theory, and electric circuits. The reader should have a background in advanced calculus and elementary probability theory, as well as a basic knowledge of measure theory and Hilbert spaces. Each chapter ends with a variety of exercises designed to help the reader further understand the material. Hui-Hsiung Kuo is the Nicholson Professor of Mathematics at Louisiana State University. He has delivered lectures on stochastic integration at Louisiana State University, Cheng Kung University, Meijo University, and University of Rome "Tor Vergata," among others. He is also the author of Gaussian Measures in Banach Spaces (Springer 1975), and White Noise Distribution Theory (CRC Press 1996), and a memoir of his childhood growing up in Taiwan, An Arrow Shot into the Sun (Abridge Books 2004)
Language
eng
Work
Publication
Extent
1 online resource (xiii, 278 pages).
Contents
  • Introduction
  • Brownian motion
  • Constructions of Brownian motion
  • Stochastic integrals
  • An extentions of stochastic integrals
  • Stochastic integrals for martingales
  • The Ito formula
  • Multiple Wiener integrals
  • Stochastic differential equations
  • Applications to finance
  • References
Isbn
9780387287201
Instance
Label
Introduction to stochastic integration
Title
Introduction to stochastic integration
Statement of responsibility
Hui-Hsiung Kuo
Creator
Subject
Language
eng
Summary
The theory of stochastic integration, also called the Ito calculus, has a large spectrum of applications in virtually every scientific area involving random functions, but it can be a very difficult subject for people without much mathematical background. The Ito calculus was originally motivated by the construction of Markov diffusion processes from infinitesimal generators. Previously, the construction of such processes required several steps, whereas Ito constructed these diffusion processes directly in a single step as the solutions of stochastic integral equations associated with the infinitesimal generators. Moreover, the properties of these diffusion processes can be derived from the stochastic integral equations and the Ito formula. This introductory textbook on stochastic integration provides a concise introduction to the Ito calculus, and covers the following topics: @* Constructions of Brownian motion; @* Stochastic integrals for Brownian motion and martingales; @* The Ito formula; @* Multiple Wiener-Ito integrals; @* Stochastic differential equations; @* Applications to finance, filtering theory, and electric circuits. The reader should have a background in advanced calculus and elementary probability theory, as well as a basic knowledge of measure theory and Hilbert spaces. Each chapter ends with a variety of exercises designed to help the reader further understand the material. Hui-Hsiung Kuo is the Nicholson Professor of Mathematics at Louisiana State University. He has delivered lectures on stochastic integration at Louisiana State University, Cheng Kung University, Meijo University, and University of Rome "Tor Vergata," among others. He is also the author of Gaussian Measures in Banach Spaces (Springer 1975), and White Noise Distribution Theory (CRC Press 1996), and a memoir of his childhood growing up in Taiwan, An Arrow Shot into the Sun (Abridge Books 2004)
Member of
Is part of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1941-
http://library.link/vocab/creatorName
Kuo, Hui-Hsiung
Dewey number
519.2/2
Index
index present
Language note
English
LC call number
QA274.22
LC item number
.K86 2006eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
NLM call number
Online Book
Series statement
Universitext
http://library.link/vocab/subjectName
  • Stochastic integrals
  • Martingales (Mathematics)
  • Stochastic Processes
  • Martingales (Mathematics)
  • Stochastic integrals
  • Martingales (Mathematics)
  • Stochastic integrals
Label
Introduction to stochastic integration, Hui-Hsiung Kuo
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 267-270) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction -- Brownian motion -- Constructions of Brownian motion -- Stochastic integrals -- An extentions of stochastic integrals -- Stochastic integrals for martingales -- The Ito formula -- Multiple Wiener integrals -- Stochastic differential equations -- Applications to finance -- References
Control code
209913511
Dimensions
unknown
Extent
1 online resource (xiii, 278 pages).
Form of item
online
Isbn
9780387287201
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/0-387-31057-6
http://library.link/vocab/ext/overdrive/overdriveId
978-0-387-28720-1
Specific material designation
remote
System control number
(OCoLC)209913511
Label
Introduction to stochastic integration, Hui-Hsiung Kuo
Publication
Bibliography note
Includes bibliographical references (pages 267-270) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction -- Brownian motion -- Constructions of Brownian motion -- Stochastic integrals -- An extentions of stochastic integrals -- Stochastic integrals for martingales -- The Ito formula -- Multiple Wiener integrals -- Stochastic differential equations -- Applications to finance -- References
Control code
209913511
Dimensions
unknown
Extent
1 online resource (xiii, 278 pages).
Form of item
online
Isbn
9780387287201
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/0-387-31057-6
http://library.link/vocab/ext/overdrive/overdriveId
978-0-387-28720-1
Specific material designation
remote
System control number
(OCoLC)209913511

Subject

Member of

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