Noncausal Stochastic Calculus

Nonfiction, Science & Nature, Mathematics
Cover of the book Noncausal Stochastic Calculus by Shigeyoshi Ogawa, Springer Japan
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Shigeyoshi Ogawa ISBN: 9784431565765
Publisher: Springer Japan Publication: July 24, 2017
Imprint: Springer Language: English
Author: Shigeyoshi Ogawa
ISBN: 9784431565765
Publisher: Springer Japan
Publication: July 24, 2017
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Japan

Cover of the book Neurogenesis in the Adult Brain II by Shigeyoshi Ogawa
Cover of the book Atlas of Posterior Fundus Changes in Pathologic Myopia by Shigeyoshi Ogawa
Cover of the book Analysis and Control of Complex Dynamical Systems by Shigeyoshi Ogawa
Cover of the book Protection of the Three Poles by Shigeyoshi Ogawa
Cover of the book Heart Replacement by Shigeyoshi Ogawa
Cover of the book Evolutionary Foundations of Economic Science by Shigeyoshi Ogawa
Cover of the book Physics of Soft Impact and Cratering by Shigeyoshi Ogawa
Cover of the book Civil Society Organization and Disaster Risk Reduction by Shigeyoshi Ogawa
Cover of the book Amebiasis by Shigeyoshi Ogawa
Cover of the book Ventricular Assist Devices in Advanced-Stage Heart Failure by Shigeyoshi Ogawa
Cover of the book Non-Cooperative Game Theory by Shigeyoshi Ogawa
Cover of the book Longitudinal Double-Spin Asymmetry of Electrons from Heavy Flavor Decays in Polarized p + p Collisions at √s = 200 GeV by Shigeyoshi Ogawa
Cover of the book Oxygen Homeostasis and Its Dynamics by Shigeyoshi Ogawa
Cover of the book Groundwater and Subsurface Environments by Shigeyoshi Ogawa
Cover of the book The Great East Japan Earthquake and Its Impact on German Firms by Shigeyoshi Ogawa
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy