Probability and Random Processes, 4/e (Paperback)
暫譯: 機率與隨機過程（第4版，平裝本）

Geoffrey Grimmett , David Stirzaker

Probability and Random Processes, 4/e (Paperback)

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商品描述

The fourth edition of this successful text provides an introduction to probability and random processes, with many practical applications. It is aimed at mathematics undergraduates and postgraduates, and has four main aims.

 

  • To provide a thorough but straightforward account of basic probability theory, giving the reader a natural feel for the subject unburdened by oppressive technicalities.
  • To discuss important random processes in depth with many examples.
  • To cover a range of topics that are significant and
    interesting but less routine.
  • To impart to the beginner some flavour of advanced work.

 

The book begins with the basic ideas common to most undergraduate courses in mathematics, statistics, and science. It ends with material usually found at graduate level, for example, Markov processes, (including Markov chain Monte Carlo), martingales, queues, diffusions, (including stochastic
calculus with Itô's formula), renewals, stationary processes (including the ergodic theorem), and option pricing in mathematical finance using the Black-Scholes formula. Further, in this new revised fourth edition, there are sections on coupling from the past, Lévy processes, self-similarity and
stability, time changes, and the holding-time/jump-chain construction of continuous-time Markov chains. Finally, the number of exercises and problems has been increased by around 300 to a total of about 1300, and many of the existing exercises have been refreshed by additional parts. The solutions
to these exercises and problems can be found in the companion volume, One Thousand Exercises in Probability, third edition, (OUP 2020).

 

 

商品描述(中文翻譯)

第四版的這本成功教材提供了機率與隨機過程的介紹，並包含許多實際應用。它的目標讀者為數學本科生和研究生，並有四個主要目標。

- 提供一個徹底但簡單明瞭的基本機率理論說明，使讀者能自然地理解這個主題，而不會被繁瑣的技術細節所困擾。
- 深入討論重要的隨機過程，並提供許多範例。
- 涵蓋一系列重要且有趣但較不常見的主題。
- 讓初學者感受到一些進階工作的風味。

本書從大多數數學、統計學和科學本科課程中常見的基本概念開始，並以通常在研究生階段出現的材料結束，例如，馬可夫過程（包括馬可夫鏈蒙地卡羅）、馬丁蓋爾、排隊、擴散（包括帶有伊藤公式的隨機微積分）、更新、平穩過程（包括遍歷定理），以及使用布萊克-斯科爾斯公式的數學金融中的選擇權定價。此外，在這個新修訂的第四版中，還增加了關於過去的耦合、勒維過程、自相似性與穩定性、時間變換，以及連續時間馬可夫鏈的持有時間/跳躍鏈構造的章節。最後，習題和問題的數量增加了約300道，總數約為1300道，並且許多現有的習題也增加了附加部分。這些習題和問題的解答可以在伴隨的書籍《機率中的一千道習題》第三版（OUP 2020）中找到。

作者簡介


Geoffrey Grimmett, Director of Research and Professor Emeritus of Mathematical Statistics, University of Cambridge, David Stirzaker, Professor Emeritus, Mathematical Institute, University of Oxford

Geoffrey Grimmett is Professor Emeritus of Mathematical Statistics at the University of Cambridge. Cambridge has been his base for pursuing probability theory and the mathematics of disordered systems since 1992. He was Master of Downing College, Cambridge from 2013-2018 and has been appointed Chair
of the Heilbronn Institute for Mathematical Research from 2020. He has written numerous research articles in probability theory and statistical mechanics, as well as three research books. With David Stirzaker and Dominic Welsh respectively, he has co-authored two successful textbooks on probability
and random processes at the undergraduate and postgraduate levels.

David Stirzaker was educated at Oxford University and Berkeley before being appointed as Fellow and Tutor in Applied Mathematics at St John's College, Oxford. He is now an Emeritus Research Fellow at St John's College, and an Emeritus Professor at the Mathematical Institute, Oxford. He has written
five textbooks on probability and random processes, two of them jointly with Geoffrey Grimmett. Most recently, (2015), he has written The Cambridge Dictionary of Probability and its Applications.

作者簡介(中文翻譯)

喬治·格里梅特（Geoffrey Grimmett），劍橋大學數學統計學研究主任及名譽教授，戴維·斯特爾扎克（David Stirzaker），牛津大學數學研究所名譽教授

喬治·格里梅特是劍橋大學數學統計學的名譽教授。自1992年以來，劍橋一直是他研究機率論和無序系統數學的基地。他於2013年至2018年擔任劍橋大學唐寧學院院長，並於2020年被任命為海爾布朗數學研究所的主席。他在機率論和統計力學方面撰寫了大量研究文章，以及三本研究書籍。與戴維·斯特爾扎克（David Stirzaker）和多米尼克·韋爾什（Dominic Welsh）分別合著了兩本成功的本科及研究生層次的機率和隨機過程教科書。

戴維·斯特爾扎克在牛津大學和伯克利接受教育，之後被任命為牛津大學聖約翰學院應用數學的研究員和導師。他現在是聖約翰學院的名譽研究員，以及牛津數學研究所的名譽教授。他撰寫了五本有關機率和隨機過程的教科書，其中兩本是與喬治·格里梅特共同編寫的。最近（2015年），他撰寫了《劍橋機率及其應用詞典》。

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