隨機過程高級教程

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.

內(nèi)容概要

　　本書是人民郵電出版社影印和翻譯出版的《隨機過程初級教程》的姊妹篇，內(nèi)容包括馬爾可夫鏈的代數(shù)方法、轉(zhuǎn)移概率的比定理及應用、連續(xù)時間馬爾可夫鏈、擴散過程、復合隨機過程、獨立同分布隨機變理部分和波動理論、排隊過程等很多主題。本書將理論與應用有機地結(jié)合在一起，取得了完美的平衡?！　”緯m用而廣，可供數(shù)學、物理學、生物學、社會學、管理學和其他工程領域的理論研究者和實踐者學習。

作者簡介

Samuel Karlin，斯坦福大學榮休教授，國際著名的應用概率學家，美國科學院院士，數(shù)理統(tǒng)計學會會士。1987年獲馮·諾伊曼獎。在生滅過程中計算平穩(wěn)分布的Karlin-McGregor定理即以他的名字命名。

書籍目錄

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

媒體關注與評論

　　“本書堪稱隨機過程教材的典范，非常透徹地討論了所有重要的主題，應用豐富，習題非常具有挑戰(zhàn)性?！薄　　狤ric Slud，馬里蘭大學教授　　“本書是通往華爾街的必備讀物。書中討論的隨機過程知識將為你理解期權(quán)定價打下堅實基礎。”　　——Amazon

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