| 書目名稱 | Noncausal Stochastic Calculus | | 編輯 | Shigeyoshi Ogawa | | 視頻video | http://file.papertrans.cn/668/667176/667176.mp4 | | 概述 | 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 noncau | | 圖書封面 |  | | 描述 | 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 It?. As is generally known, It? 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.. | | 出版日期 | Book 2017 | | 關(guān)鍵詞 | Noncausal; Stochastic Calculus; random variable; stochastic derivative; principle of causality | | 版次 | 1 | | doi | https://doi.org/10.1007/978-4-431-56576-5 | | isbn_softcover | 978-4-431-56825-4 | | isbn_ebook | 978-4-431-56576-5 | | copyright | Springer Japan KK 2017 |
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