Probability and Random Processes, 4/e (Paperback)

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)

這本成功的教材第四版介紹了概率和隨機過程，並提供了許多實際應用。它針對數學本科和研究生，有四個主要目標。


  • 提供一個徹底但簡單的基礎概率理論，讓讀者對主題有自然的感覺，不受繁瑣的技術約束。

  • 深入討論重要的隨機過程，並提供許多例子。

  • 涵蓋一系列重要且有趣但不常見的主題。

  • 讓初學者感受到高級工作的風味。

這本書從大多數數學、統計和科學本科課程中常見的基本概念開始，並以研究生水平的材料結束，例如馬爾可夫過程（包括馬爾可夫鏈蒙特卡羅）、鞍點、隊列、擴散（包括帶有伊諾公式的隨機微積分）、更新、平穩過程（包括遞歸定理）以及使用Black-Scholes公式的數學金融期權定價。此外，在這個新修訂的第四版中，增加了關於過去的耦合、Lévy過程、自相似性和穩定性、時間變換以及連續時間馬爾可夫鏈的持續時間/跳躍鏈構造的部分。最後，練習題和問題的數量增加了約300個，總數約為1300個，並且許多現有的練習題增加了額外的部分。這些練習和問題的解答可以在配套的書籍《概率一千道練習題》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)

Geoffrey Grimmett，劍橋大學數學統計學研究主任和名譽教授，David Stirzaker，牛津大學數學研究所名譽教授。

Geoffrey Grimmett是劍橋大學數學統計學的名譽教授。自1992年以來，劍橋一直是他從事概率論和無序系統數學研究的基地。他曾擔任劍橋大學唐寧學院院長（2013-2018年），並於2020年被任命為海爾布隆數學研究所主席。他在概率論和統計力學領域發表了許多研究論文，並出版了三本研究書籍。他與David Stirzaker和Dominic Welsh合著了兩本成功的本科和研究生概率和隨機過程教材。

David Stirzaker在牛津大學和伯克利接受教育後，被任命為牛津大學聖約翰學院應用數學研究員和導師。他現在是聖約翰學院的名譽研究員和牛津大學數學研究所的名譽教授。他撰寫了五本概率和隨機過程教材，其中兩本與Geoffrey Grimmett合著。最近（2015年），他撰寫了《劍橋概率詞典及其應用》。

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