随机过程高级教程

作者简介

《随机过程高级教程(英文版)》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。

书籍目录

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

前言

　　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.

内容概要

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。

Howard M.Taylor，康奈尔大学荣休教授，国际著名的应用概率学家。

媒体关注与评论

　　“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

图书封面

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