随机过程高级教程
2009-1
人民邮电出版社
Samuel Karlin)卡林 (美国)(Howard M.Taylor
542
504000
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This Second Course continues the development of the theory and applications of stochastic processes as promised in the preface of A First Course. We emphasize a careful treatment of basic structures in stochastic processes in symbiosis with the analysis of natural classes of stochastic processes arising from the biological， physical， and social sciences. Apart from expanding on the topics treated in the first edition of this work but not incorporated in A First Course， this volume presents an extensive introductory account of the fundamental concepts and methodology of diffusion processes and the closely allied theory of stochastic differential equations and stochastic integrals. A multitude of physical， engineering， biological， social， and managerial phenomena are either well approximated or reasonably modeled by diffusion processes; and modern approaches to diffusion processes and stochastic differential equations provide new perspectives and techniques impinging on many subfields of pure and applied mathematics， among them partial differential equations， dynamical systems， optimal control problems， statistical decision procedures， operations research， studies of economic systems， population genetics， and ecology models. A new chapter discusses the elegant and far-reaching distributional formulas now available for a wide variety of functionas （e.g.， first-passage time， maximum， order statistics， occupation time） of the process of sums of independent random variables. The identities， formulas， and results in this chapter have important appfications in queueing and renewal theory， for statistical decision procedures， and elsewhere.
本书是人民邮电出版社影印和翻译出版的《随机过程初级教程》的姊妹篇，内容包括马尔可夫链的代数方法、转移概率的比定理及应用、连续时间马尔可夫链、扩散过程、复合随机过程、独立同分布随机变理部分和波动理论、排队过程等很多主题。本书将理论与应用有机地结合在一起，取得了完美的平衡。 本书适用而广，可供数学、物理学、生物学、社会学、管理学和其他工程领域的理论研究者和实践者学习。
Samuel Karlin，斯坦福大学荣休教授，国际著名的应用概率学家，美国科学院院士，数理统计学会会士。1987年获冯·诺伊曼奖。在生灭过程中计算平稳分布的Karlin-McGregor定理即以他的名字命名。
Chapter 10 ALGEBRAIC METHODS IN MARKOV CHAINS 1.Preliminaria 2.Relations of Eigenvalues and Recurrence Claum 3.Periodic Classes 4.Special Computational Methods in Markov Chains 5.Examples 6.Applications to Coin Tomin9 Elementary Problems Problermt Nores References Chapter 11 RATIO THEoREMS oF TRANSITl0N PROBABILITIES AND APPLICATl0NS 1.Taboo Probabilities 2.RatioTheorems 3.Existence of Generalized Stationary Distributions 4.Interpretation of Generalized Stationary Distributions 5.Regular, Superregular, and Subregular Sequences for Markov Chains 6.Stopping Rule Problems Elementary Problems Problems Notes ReferencesChapter 12 SUMS OF INDEPENDENT RANDOM VARIABLES AS A MARKOV CHAIN 1.Recurrence Properties of Sums of Independent Random Variables 2.Local Limit Theorems 3.Right Regular Sequences for the Markov Chain 4.The Discrete Renewal Theorem Elementary Problems Problems Notes ReferencesChapter 13 ORDER STATISTICS, POISSON PROCESSES, ANDAPPLICATIONS 1.Order Statistics and Their Relation to Poisson Processes 2.The Ballot Problem 3.Empirical Distribution Functions 4.Some Limit Distributions for Empirical Distribution Functions Elementary Problems Problems Notes ReferencesChapter 14 CONTINUOUS TIME MARKOV CHAINS 1.Differentiability Properties of Transition Probabilities 2.Conservative Processes and the Forward and Backward Differential Equations 3.Construction of a Continuous Time Markov Chain from Its Infinitesimal Parameters ……Chapter 15 DIFFUSION PROCESSESChapter 16 COMPOUNDING STOCHASTIC PROCESSESChapter 17 FLUCTU ATION THEORY OF PARTIAL SUMS OF INDEPENDENT IDENTICALLY DIXTRIBUTED RANDOM VARIABLESChapter 18 QUEUEING PROCESSESMISCELLANEOUS PROBLEMSInedx
“本书堪称随机过程教材的典范，非常透彻地讨论了所有重要的主题，应用丰富，习题非常具有挑战性。” ——Eric Slud，马里兰大学教授 “本书是通往华尔街的必备读物。书中讨论的随机过程知识将为你理解期权定价打下坚实基础。” ——Amazon
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无论是内容还是印刷都一级棒~经典的随机过程书，推荐！
实际上个人感觉这本书的名字不是很好.因为英文名是secondcourseofstochasticprocess.也就是说实际上还有firstcourses,是同属一个系列的.内容实在太经典了.个人感觉现在看随即过程的基本都是学金融到了一定程度,所谓的"学习障"的时候,返回来寻求更高的突破.当然突破后所带来的感觉和所获得的收益,相比各位都有所体会吧.如果你是这个想法,那么恭喜你,你来对地方了.这就是你想要的
内容翔实，结构清晰
hen haode