圖書標籤: 數學 金融 金融數學 金融工程 Mathematics 統計學 quant Probability
发表于2024-07-13
Brownian Motion and Stochastic Calculus pdf epub mobi txt 電子書 下載 2024
A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.
如所有經典教材一樣包羅萬象
評分題暫時沒時間刷瞭。做Diffusion的我覺得都需要至少過一遍這本書。
評分隨機分析與應用的教材,大二學的時候覺得真的難啊……
評分我喜歡他的理論化係統化和有例題有講解的態度。(各位數學大牛很喜歡把很多東西看成"顯然",殊不知很多"顯然的"對於初學者實在是很難。)雖然我覺得他在錶述上有些羅嗦,而且整本書結構結構不適很閤理,從Stopping time開始,然後又突然說Brownian motion,然後又突然講Martingale. 既然我們要做的是Calculus,當然就要以Martingale作為核心理論逐次展開,這樣纔能讓人比較容易理解到底是要討論什麼啊。
評分最近在讀Sannikov的論文,引用瞭很多這書裏習題的結論,於是打迴重讀瞭,對於想瞭解連續時間框架的,這書要全讀/題全刷。
这本书的特点是非常全面,一切关于布朗运动的知识、连续半鞅随机积分ITO公式的各种变形,都可以从该书找到,不是正文就是习题。写得也极具启发性,比如和一个stopping time相联系的sigma代数filtration,一般的书都是直接给出个定义,只有这本书解释了为什么会有这样的定...
評分Brownian Motion and Stochastic Calculus pdf epub mobi txt 電子書 下載 2024