| 书目名称 | Introduction to Stochastic Integration | | 编辑 | Hui-Hsiung Kuo | | 视频video | http://file.papertrans.cn/475/474226/474226.mp4 | | 概述 | Provides a concise introduction to the theory of stochastic integration, also called the Ito calculus.Closes the gap between more technically advanced books like Karatzas and Shreve (Springer) and les | | 丛书名称 | Universitext | | 图书封面 |  | | 描述 | In the Leibniz–Newton calculus, one learns the di?erentiation and integration of deterministic functions. A basic theorem in di?erentiation is the chain rule, which gives the derivative of a composite of two di?erentiable functions. The chain rule, when written in an inde?nite integral form, yields the method of substitution. In advanced calculus, the Riemann–Stieltjes integral is de?ned through the same procedure of “partition-evaluation-summation-limit” as in the Riemann integral. In dealing with random functions such as functions of a Brownian motion, the chain rule for the Leibniz–Newton calculus breaks down. A Brownian motionmovessorapidlyandirregularlythatalmostallofitssamplepathsare nowhere di?erentiable. Thus we cannot di?erentiate functions of a Brownian motion in the same way as in the Leibniz–Newton calculus. In 1944 Kiyosi Itˆ o published the celebrated paper “Stochastic Integral” in the Proceedings of the Imperial Academy (Tokyo). It was the beginning of the Itˆ o calculus, the counterpart of the Leibniz–Newton calculus for random functions. In this six-page paper, Itˆ o introduced the stochastic integral and a formula, known since then as Itˆ o’s formula. The Itˆ o fo | | 出版日期 | Textbook 2006 | | 关键词 | Brownian motion; Gaussian measure; Martingale; Measure; Probability theory; Stochastic Differential Equat | | 版次 | 1 | | doi | https://doi.org/10.1007/0-387-31057-6 | | isbn_softcover | 978-0-387-28720-1 | | isbn_ebook | 978-0-387-31057-2Series ISSN 0172-5939 Series E-ISSN 2191-6675 | | issn_series | 0172-5939 | | copyright | Springer-Verlag New York 2006 |
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