Authors:
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
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Table of contents (10 chapters)
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Front Matter
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Back Matter
About this book
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.
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Authors and Affiliations
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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