Stochastic Analysis and Diffusion Processes (Paperback)
暫譯: 隨機分析與擴散過程(平裝本)
Gopinath Kallianpur
- 出版商: Oxford University
- 出版日期: 2014-02-06
- 售價: $970
- 貴賓價: 9.8 折 $951
- 語言: 英文
- 頁數: 368
- 裝訂: Paperback
- ISBN: 0199657076
- ISBN-13: 9780199657070
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相關分類:
機率統計學 Probability-and-statistics、物理學 Physics
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商品描述
Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details.
Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Ito formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book.
The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions.
Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.
商品描述(中文翻譯)
隨機分析與擴散過程提供了一個簡單的數學介紹,涵蓋隨機微積分及其應用。本書建立了基本理論,並仔細闡述了隨機分析中的重要研究方向。隨機分析的廣度與力量,以及擴散過程的隨機行為,均在不妥協數學細節的情況下進行說明。
本書從隨機過程的構造開始,介紹布朗運動和馬丁蓋爾。接著,本書構建隨機積分,建立伊藤公式,並討論其應用。接下來,重點放在隨機微分方程(SDEs)上,這些方程在建模受隨機力擾動的物理現象時會出現。擴散過程是隨機微分方程的解,並構成本書的主要主題。
斯特魯克-瓦爾丹馬丁蓋爾問題、擴散過程與偏微分方程之間的聯繫、隨機微分方程的高斯解,以及具有跳躍的馬可夫過程,將在後續章節中介紹。本書以對重要研究主題的仔細處理作為結尾,例如不變測度、遍歷行為和擴散的大偏差原理。
全書提供了示例以說明概念和結果。此外,每章末尾還提供了練習題,幫助讀者更好地理解這些概念。本書是為對隨機過程及其應用感興趣的研究生、年輕研究人員和應用科學家所撰寫。假設讀者已熟悉研究生水平的概率論。本書可作為隨機分析研究生課程的教材。