Measure Theory, Probability, and Stochastic Processes
Le Gall, Jean-François
- 出版商: Springer
- 出版日期: 2022-10-30
- 售價: $3,110
- 貴賓價: 9.5 折 $2,955
- 語言: 英文
- 頁數: 406
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031142047
- ISBN-13: 9783031142048
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商品描述
This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis.
Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illuminating exercises of varying difficulty. Some basic facts from functional analysis, in particular on Hilbert and Banach spaces, are included in the appendix.
Measure Theory, Probability, and Stochastic Processes is an ideal text for readers seeking a thorough understanding of basic probability theory. Students interested in learning more about Brownian motion, and other continuous-time stochastic processes, may continue reading the author's more advanced textbook in the same series (GTM 274).
商品描述(中文翻譯)
這本教科書向讀者介紹現代概率論的基本概念。唯一的先決條件是對實分析有一定的了解。本書強調馬丁格爾和馬可夫鏈以及布朗運動和調和函數之間的聯繫，為概率和其他分析領域之間豐富的相互作用提供了一個介紹。
本書分為三個部分，第一部分嚴謹地介紹了測度論，並以概率應用為目標。第二部分集中介紹了概率論的基本概念，如隨機變量、獨立性、條件期望和隨機變量的不同收斂類型。在第三部分中，讀者將遇到三個重要的隨機過程類別：離散時間馬丁格爾、可數狀態馬可夫鏈和布朗運動。每章結束時都附有一些具有不同難度的啟發性練習題。附錄中包含了一些來自函數分析的基本事實，特別是關於希爾伯特和巴拿赫空間的知識。
《測度論、概率和隨機過程》是一本理想的教材，適合那些希望深入了解基本概率論的讀者。對於想要了解更多關於布朗運動和其他連續時間隨機過程的學生，可以繼續閱讀本系列作者的更高級教科書（GTM 274）。
作者簡介
Jean-François Le Gall is Professor of Mathematics at the University of Paris-Saclay in France. As one of the leading experts in probability theory, he has done extensive research on stochastic processes, including Brownian motion, random trees, random planar maps, and other related objects. His research accomplishments have been recognized with various awards, most recently the Wolf prize. He is the author of two successful textbooks on Brownian Motion, Martingales, and Stochastic Calculus (2016) in the Graduate Texts in Mathematics series and Spatial Branching Processes, Random Snakes and Partial Differential Equations (1999) in the Lectures in Mathematics, ETH Zürich series.
作者簡介(中文翻譯)
Jean-François Le Gall是法國巴黎-索克萊大學的數學教授。作為概率論的領先專家之一，他在隨機過程方面進行了廣泛的研究，包括布朗運動、隨機樹、隨機平面圖和其他相關對象。他的研究成果獲得了多個獎項的認可，最近獲得了沃爾夫獎。他是《布朗運動、鞅和隨機微積分》（2016年）和《空間分支過程、隨機蛇和偏微分方程》（1999年）兩本成功的教科書的作者，分別屬於Graduate Texts in Mathematics系列和Lectures in Mathematics, ETH Zürich系列。
