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Noncausal stochastic calculus

Ogawa, Shigeyoshi.

Noncausal stochastic calculus

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Noncausal stochastic calculusby Shigeyoshi Ogawa.
作者:	Ogawa, Shigeyoshi.
出版者:	Tokyo :Springer Japan :2017.
面頁冊數:	xii, 210 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Stochastic analysis.
電子資源:	http://dx.doi.org/10.1007/978-4-431-56576-5
ISBN:	9784431565765$q(electronic bk.)

Noncausal stochastic calculus
Ogawa, Shigeyoshi.

Noncausal stochastic calculus[electronic resource] /by Shigeyoshi Ogawa. - Tokyo :Springer Japan :2017. - xii, 210 p. :ill., digital ;24 cm.

1 Introduction - Why the Causality? -- 2 Preliminary - Causal calculus -- 3 Noncausal Calculus -- 4 Noncausal Integral and Wiener Chaos -- 5 Noncausal SDEs -- 6 Brownian Particle Equation -- 7 Noncausal SIE -- 8 Stochastic Fourier Transformation -- 9 Appendices to Chapter 2 -- 10 Appendices 2 - Comments and Proofs -- Index.

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.

ISBN: 9784431565765$q(electronic bk.)

Standard No.: 10.1007/978-4-431-56576-5doiSubjects--Topical Terms:

183332
Stochastic analysis.

LC Class. No.: QA274.2

Dewey Class. No.: 519.22

Noncausal stochastic calculus
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505 0 $a 1 Introduction - Why the Causality? -- 2 Preliminary - Causal calculus -- 3 Noncausal Calculus -- 4 Noncausal Integral and Wiener Chaos -- 5 Noncausal SDEs -- 6 Brownian Particle Equation -- 7 Noncausal SIE -- 8 Stochastic Fourier Transformation -- 9 Appendices to Chapter 2 -- 10 Appendices 2 - Comments and Proofs -- Index.
520 $a 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.
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