Skip to main content
SpringerLink
Log in

Noncausal Stochastic Calculus

  • Book
  • © 2017

Overview

Authors:
  1. Shigeyoshi Ogawa

    1. Department of Mathematical Sciences, Ritsumeikan University, Kusatsu, Japan

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Is the first book on a stochastic calculus of noncausal nature based on the noncausal stochastic integral introduced by the author in 1979

  • Begins with the study of fundamental properties of the noncausal stochastic integral by the author

  • Refers to the relation with other stochastic integrals, causal or not, such as the symmetric integrals and the anticipative integral by A. Skorokhod

  • Develops the theory along with the study of various noncausal problems in stochastic calculus, most of which are about functional equations

  • Includes supplementary material: sn.pub/extras

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (10 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Introduction – Why the Causality?

    • Shigeyoshi Ogawa
    Pages 1-10

  3. Preliminary – Causal Calculus

    • Shigeyoshi Ogawa
    Pages 11-50

  4. Noncausal Calculus

    • Shigeyoshi Ogawa
    Pages 51-81

  5. Noncausal Integral and Wiener Chaos

    • Shigeyoshi Ogawa
    Pages 83-89

  6. Noncausal SDEs

    • Shigeyoshi Ogawa
    Pages 91-107

  7. Brownian Particle Equation

    • Shigeyoshi Ogawa
    Pages 109-125

  8. Noncausal SIE

    • Shigeyoshi Ogawa
    Pages 127-137

  9. Stochastic Fourier Transformation

    • Shigeyoshi Ogawa
    Pages 139-170

  10. Appendices to Chapter 2

    • Shigeyoshi Ogawa
    Pages 171-180

  11. Appendices 2 – Comments and Proofs

    • Shigeyoshi Ogawa
    Pages 181-201

  12. Back Matter

    Pages 203-210
    Download chapter PDF
Back to top

Keywords

About this book

This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale.


The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979.


After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but also its growing possibility as a tool for modeling and analysis in every domain of mathematical sciences. The reader may find there many open problems as well.

Reviews

“The book is well and precisely written with many details and comments. In my opinion, S. Ogawa’s book is very interesting for people working on stochastic calculus, stochastic differential equations and their applications.” (Anna Karczewska, zbMATH 1381.60003, 2018)

Authors and Affiliations

  • Department of Mathematical Sciences, Ritsumeikan University, Kusatsu, Japan

    Shigeyoshi Ogawa

Bibliographic Information

  • Book Title: Noncausal Stochastic Calculus

  • Authors: Shigeyoshi Ogawa

  • DOI: https://doi.org/10.1007/978-4-431-56576-5

  • Publisher: Springer Tokyo

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Japan KK 2017

  • Hardcover ISBN: 978-4-431-56574-1Published: 04 August 2017

  • Softcover ISBN: 978-4-431-56825-4Published: 12 August 2018

  • eBook ISBN: 978-4-431-56576-5Published: 24 July 2017

  • Edition Number: 1

  • Number of Pages: XII, 210

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Mathematics, general

Publish with us

Policies and ethics

Back to top

Search

Navigation