Markov Chains: Gibbs Fields, Monte Carlo Simulation and Queues (Texts in Applied Mathematics, 31) 2nd ed. 2020 版本(Hardcover )

This book discusses both the theory and applications of Markov chains. The author studies both discrete-time and continuous-time chains and connected topics such as finite Gibbs fields, non-homogeneous Markov chains, discrete time regenerative processes, Monte Carlo simulation, simulated annealing, and queueing networks are also developed in this accessible and self-contained text. The text is firstly an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level. Its primary objective is to initiate the student to the art of stochastic modelling. The treatment is mathematical, with definitions, theorems, proofs and a number of classroom examples which help the student to fully grasp the content of the main results. Problems of varying difficulty are proposed at the close of each chapter. The text is motivated by significant applications and progressively brings the student to the borders of contemporary research. Students and researchers in operations research and electrical engineering as well as in physics, biology and the social sciences will find this book of interest.

本書討論馬可夫鏈的理論和應用。作者研究離散時間和連續時間的鏈，並涉及有限吉布斯場、非齊次馬可夫鏈、離散時間再生過程、蒙特卡羅模擬、模擬退火和排隊網絡等相關主題。這本易於理解且自成一體的教材首先介紹了本科或研究生入門水平的隨機過程理論。其主要目標是引導學生進入隨機建模的藝術。教材以數學方式呈現，包括定義、定理、證明和一些課堂示例，有助於學生充分理解主要結果的內容。每章末尾提出了各種難度的問題。本書以重要應用為動力，逐步將學生引向當代研究的邊緣。運籌學和電氣工程以及物理學、生物學和社會科學的學生和研究人員將對本書感興趣。

Pierre Brémaud graduated from the École Polytechnique and obtained his Doctorate in Mathematics from the University of Paris VI and his PhD from the department of Electrical Engineering and Computer Science at the University of California, Berkeley. He is a major contributor to the theory of stochastic processes and their applications, and has authored or co-authored several reference books and textbooks.

Pierre Brémaud畢業於法國巴黎高等理工學院，並在巴黎第六大學數學系獲得博士學位，同時也在加州大學伯克利分校電機工程與計算機科學系獲得博士學位。他是隨機過程及其應用理論的重要貢獻者，並撰寫或合著了多本參考書籍和教科書。