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 Modern Methodology and Applications in Spatial-Temporal Modeling by Shigeyoshi Ogawa
Cover of the book High-Resolution Spin-Resolved Photoemission Spectrometer and the Rashba Effect in Bismuth Thin Films by Shigeyoshi Ogawa
Cover of the book Methods in Neuroethological Research by Shigeyoshi Ogawa
Cover of the book The Impact of Applications on Mathematics by Shigeyoshi Ogawa
Cover of the book Oral Cancer by Shigeyoshi Ogawa
Cover of the book Progress in Social Psychiatry in Japan by Shigeyoshi Ogawa
Cover of the book Space-Time Foliation in Quantum Gravity by Shigeyoshi Ogawa
Cover of the book Nonlinearity, Bounded Rationality, and Heterogeneity by Shigeyoshi Ogawa
Cover of the book Total Synthesis of Bioactive Natural Products by Palladium-Catalyzed Domino Cyclization of Allenes and Related Compounds by Shigeyoshi Ogawa
Cover of the book Morpho-functional Machines: The New Species by Shigeyoshi Ogawa
Cover of the book Nanobiosensors and Nanobioanalyses by Shigeyoshi Ogawa
Cover of the book Cardiac Mechanics and Function in the Normal and Diseased Heart by Shigeyoshi Ogawa
Cover of the book Serviceology for Designing the Future by Shigeyoshi Ogawa
Cover of the book AdS/CFT Duality User Guide by Shigeyoshi Ogawa
Cover of the book Theory of Hypergeometric Functions 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