应用随机过程:概率模型导论(英文影印版.第9版)

　　本书叙述深入浅出，涉及面广。主要内容有随机变量、条件概率及条件期望、离散及连续马尔可夫链、指数分布、泊松过程、布朗运动及平稳过程、更新理论及排队论等；也包括了随机过程在物理、生物、运筹、网络、遗传、经济、保险、金融及可靠性中的应用。特别是有关随机模拟的内容，给随机系统运行的模拟计算提供了有力的工具。除正文外，本书有约700道习题，其中带星号的习题还提供了解答。
　　 本书可作为概率论与统计、计算机科学、保险学、物理学、社会科学、生命科学、管理科学与工程学等专业随机过程基础课教材。

1.introduction to probability theory
1.1.introduction
1.2.sample space and events
1.3.probabilities defined on events
1.4.conditional probabilities
1.5.independent events
1.6.bayes' formula
exercises
references
2.random variables
2.1.random variables
2.2.discrete random variables
2.3.continuous random variables
2.4.expectation of a random variable
2.5.jointly distributed random variables
2.6.moment generating functions
2.7.limit theorems
2.8.stochastic processes
exercises
references

　　This text is intended as an introduction to elementary probability theory and stochastic processes. It is particularly well suited for those wanting to see how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research.
　　It is generally felt that there are two approaches to the study of probability theory. One approach is heuristic and nonrigorous and attempts to develop in the student an intuitive feel for the subject which enables him or her to "think probabilistically." The other approach attempts a rigorous development of probability by using the tools of measure theory. It is the first approach that is employed in this text. However, because it is extremely important in both understanding and applying probability theory to be able to "think probabilistically," this text should also be useful to students interested primarily in the second approach..
　　New to This Edition
　　The ninth edition contains the following new sections.
　　●Section 3.7 is concerned with compound random variables of the form SN＝∑Ni=1, where N is independent of the sequence of independent and identically distributed random variables Xi, i≥1. It starts by deriving a general identity concerning compound random variables, as well as a corollary of that identity in the case where the Xi are positive and integer.valued. The corollary is then used in subsequent subsections to obtain recurslve formulas for the probability mass function of SN, when N is a Poisson distribution (Subsection 3.7.1), a binomial distribution (Subsection 3.7.2), or a negative binomial distribution (Subsection 3.7.3).
　　● Section 4.11 deals with hidden Markov chains. These models suppose that a random signal is emitted each time a Markov chain enters a state, with the distribution of the signal depending on the state entered. The Markov chain is hidden in the sense that it is supposed that only the signals and not the underlying states of the chain are observable. As part of our analysis of these models we present, in Subsection 4.11.1, the Viterbi algorithm for determining the most probable sequence of first n states, given the first n signals.
　　●Section 8.6.4 analyzes the Poisson arrival single server queue under the assumption that the working server will randomly break down and need repair.
　　There is also new material in almost all chapters. Some of the more significant additions being the following.
　　● Example 5.9, which is concerned with the expected number of normal cells that survive until all cancer cells have been killed. The example supposes that each cell has a weight, and the probability that a given surviving cell is the next cell killed is proportional to its weight.
　　●A new approach--based on time sampling of a Poisson process---is presented in Subsection 5.4.1 for deriving the probability mass function of the number of events of a nonhomogeneous Poisson process that occur in any specified time interval.
　　●There is additional material in Section 8.3 concerning the M/M/1 queue. Among other things, we derive the conditional distribution of the number of customers originally found in the system by a customer who spends a time t in the system before departing. (The conditional distribution is Poisson.) In Example 8.3, we illustrate the inspection paradox, by obtaining the probability distribution of the number in the system as seen by the first arrival after some specified time.
　　Course
　　Ideally, this text would be used in a one-year course in probability models. Other possible courses would be a one-semester course in introductory probability theory (involving Chapters 1-3 and parts of others) or a course in elementary stochastic processes. The textbook is designed to be flexible enough to be used in a variety of possible courses. For example, I have used Chapters 5 and 8, with smatterings from Chapters 4 and 6, as the basis of an introductory course in queueing theory.
　　Examples and Exercises
　　Many examples are worked out throughout the text, and there are also a large number of exercises to be solved by students. More than 100 of these exercises have been starred and their solutions provided at the end of the text. These starred problems can be used for independent study and test preparation. An Instructor's Manual, containing solutions to all exercises, is available free to instructors who adopt the book for class.
　　Organization
　　hapters 1 and 2 deal with basic ideas of probability theory. In Chapter 1 an axiomatic framework is presented, while in Chapter 2 the important concept of a random variable is introduced. Subsection 2.6.1 gives a simple derivation ofthe joint distribution of the sample mean and sample variance of a normal data sample.
　　Chapter 3 is concerned with the subject matter of conditional probability and conditional expectation. "Conditioning" is one of the key tools of probability theory, and it is stressed throughout the book. When properly used, conditioning often enables us to easily solve problems that at first glance seem quite difficult. The final section of this chapter presents applications to (1) a computer list problem, (2) a random graph, and (3)the Polya urn model and its relation to the BoseEinstein distribution. Subsection 3.6.5 presents k-record values and the surprising Ignatov's theorem...
　　In Chapter 4 we come into contact with our first random, or stochastic, process, known as a Markov chain, which is widely applicable to the study of many realworld phenomena. Applications to genetics and production processes are presented. The concept of time reversibility is introduced and its usefulness illustrated. Subsection 4 5.3 presents an analysis, based on random walk theory, of a probabilistic algorithm for the satisfiability problem. Section 4.6 deals with the mean times spent in transient states by a Markov chain. Section 4.9 introduces Markov chain Monte Carlo methods. In the final section we consider a model for optimally making decisions known as a Markovian decision process.
　　In Chapter 5 we are concerned with a type of stochastic process known as a counting process. In particular, we study a kind of counting process known as a Poisson process. The intimate relationship between this process and the exponential distribution is discussed. New derivations for the Poisson and nonhomogeneous Poisson processes are discussed. Examples relating to analyzing greedy algorithms, minimizing highway encounters, collecting coupons, and tracking the AIDS virus, as well as material on compound Poisson processes, are included in this chapter. Subsection 5.2.4 gives a simple derivation of the convolution of exponential random variables.