应用随机过程

出版时间：2011-2  出版社：人民邮电出版社  作者：罗斯,Sheldon M. Ross  页数：784  
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内容概要

《应用随机过程:概率模型导论(英文版·第10版)》由Sheldon
M.Ross所著，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，《应用随机过程——概率模型导论(第10版:英文版)》有约700道习题，其中带星号的习题还提供了解答。
《应用随机过程:概率模型导论(英文版·第10版)》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的随机过程基础课教材。

作者简介

罗斯，Sheldon
M.Ross国际知名概率与统计学家，南加州大学工业工程与运筹系系主任。1968年博士毕业于斯坦福大学统计系，曾在加州大学伯克利分校任教多年。研究领域包括：随机模型．仿真模拟、统计分析、金融数学等：Ross教授著述颇丰，他的多种畅销数学和统计教材均产生了世界性的影响，如Simulation(《统计模拟》)、Introduction
to Probability Models(《应用随机过程：概率模型导论》)等（均由人民邮电出版社出版）。

书籍目录

1 introduction to probability theory 1
1.1 introduction 1
1.2 sample space and events 1
1.3 probabilities defined on events 4
1.4 conditional probabilities 7
1.5 independent events 10
1.6 bayes' formula 12
exercises 15
references 20
2 random variables 21
2.1 random variables 21
2.2 discrete random variables 25
2.2.1 the bernoulli random variable
26
2.2.2 the binomial random variable 27
2.2.3 the geometric random variable
29
2.2.4 the poisson random variable 30
2.3 continuous random variables 31
2.3.1 the uniform random variable 32
2.3.2 exponential random variables 34
2.3.3 gamma random variables 34
2.3.4 normal random variables 34
2.4 expectation of a random variable 36
2.4.1 the discrete case 36
2.4.2 the continuous case 38
2.4.3 expectation of a function of a random
variable 40
2.5 jointly distributed random variables 44
2.5.1 joint distribution functions 44
2.5.2 independent random variables 48
2.5.3 covariance and variance of sums of
random variables 50
2.5.4 joint probability distribution of
functions of randomvariables 59
2.6 moment generating functions 62
2.6.1 the joint distribution of the sample
mean and sample variance from a normal population 71
2.7 the distribution of the number of events that occur
74
2.8 limit theorems 77
2.9 stochastic processes 84
exercises 86
references 95
3 conditional probability and conditional expectation 97
3.1 introduction 97
3.2 the discrete case 97
3.3 the continuous case 102
3.4 computing expectations by conditioning 106
3.4.1 computing variances by conditioning
117
3.5 computing probabilities by conditioning 122
3.6 some applications 140
3.6.1 a list model 140
3.6.2 a random graph 141
3.6.3 uniform priors, polya's urn model,
and bose-einstein statistics 149
3.6.4 mean time for patterns 153
3.6.5 the k-record values of discrete
random variables 157
3.6.6 left skip free random walks 160
3.7 an identity for compound random variables 166
3.7.1 poisson compounding distribution
169
3.7.2 binomial compounding distribution
171
3.7.3 a compounding distribution related to
the negative binomial 172
exercises 173
4 markov chains 191
4.1 introduction 191
4.2 chapman-kolmogorov equations 195
4.3 classification of states 204
4.4 limiting probabilities 214
4.5 some applications 230
4.5.1 the gambler's ruin problem 230
4.5.2 a model for algorithmic efficiency
234
4.5.3 using a random walk to analyze a
probabilistic algorithm for the satisfiability problem 237
4.6 mean time spent in transient states 243
4.7 branching processes 245
4.8 time reversible markov chains 249
4.9 markov chain monte carlo methods 260
4.10 markov decision processes 265
4.11 hidden markov chains 269
4.11.1 predicting the states 273
exercises 275
references 290
5 the exponential distribution and the poisson process 291
5.1 introduction 291
5.2 the exponential distribution 292
5.2.1 definition 292
5.2.2 properties of the exponential
distribution 294
5.2.3 further properties of the exponential
distribution 301
5.2.4 convolutions of exponential random
variables 308
5.3 the poisson process 312
5.3.1 counting processes 312
5.3.2 definition of the poisson process
313
5.3.3 interarrival and waiting time
distributions 316
5.3.4 further properties of poisson
processes 319
5.3.5 conditional distribution of the
arrival times 325
5.3.6 estimating software reliability
336
5.4 generalizations of the poisson process 339
5.4.1 nonhomogeneous poisson process
339
5.4.2 compound poisson process 346
5.4.3 conditional or mixed poisson
processes 351
exercises 354
references 370
6 continuous-time markov chains 371
6.1 introduction 371
6.2 continuous-time markov chains 372
6.3 birth and death processes 374
6.4 the transition probability function pij (t)
381
6.5 limiting probabilities 390
6.6 time reversibility 397
6.7 uniformization 406
6.8 computing the transition probabilities 409
exercises 412
references 419
7 renewal theory and its applications 421
7.1 introduction 421
7.2 distribution of n(t) 423
7.3 limit theorems and their applications 427
7.4 renewal reward processes 439
7.5 regenerative processes 447
7.5.1 alternating renewal processes
450
7.6 semi-markov processes 457
7.7 the inspection paradox 460
7.8 computing the renewal function 463
7.9 applications to patterns 466
7.9.1 patterns of discrete random variables
467
7.9.2 the expected time to a maximal run of
distinct values 474
7.9.3 increasing runs of continuous random
variables 476
7.10 the insurance ruin problem 478
exercises 484
references 495
8 queueing theory 497
8.1 introduction 497
8.2 preliminaries 498
8.2.1 cost equations 499
8.2.2 steady-state probabilities 500
8.3 exponential models 502
8.3.1 a single-server exponential queueing
system 502
8.3.2 a single-server exponential queueing
system having finite capacity 511
8.3.3 birth and death queueing models
517
8.3.4 a shoe shine shop 522
8.3.5 a queueing system with bulk service
524
8.4 network of queues 527
8.4.1 open systems 527
8.4.2 closed systems 532
8.5 the system m/g/1 538
8.5.1 preliminaries: work and another cost
identity 538
8.5.2 application of work to m/g/1
539
8.5.3 busy periods 540
8.6 variations on the m/g/1 541
8.6.1 the m/g/1 with random-sized batch
arrivals 541
8.6.2 priority queues 543
8.6.3 an m/g/1 optimization example
546
8.6.4 the m/g/1 queue with server breakdown
550
8.7 the model g/m/1 553
8.7.1 the g/m/1 busy and idle periods
558
8.8 a finite source model 559
8.9 multiserver queues 562
8.9.1 erlang's loss system 563
8.9.2 the m/m/k queue 564
8.9.3 the g/m/k queue 565
8.9.4 the m/g/k queue 567
exercises 568
references 578
9 reliability theory 579
9.1 introduction 579
9.2 structure functions 580
9.2.1 minimal path and minimal cut sets
582
9.3 reliability of systems of independent components
586
9.4 bounds on the reliability function 590
9.4.1 method of inclusion and exclusion
591
9.4.2 second method for obtaining bounds on
r(p) 600
9.5 system life as a function of component lives
602
9.6 expected system lifetime 610
9.6.1 an upper bound on the expected life
of a parallel system 614
9.7 systems with repair 616
9.7.1 a series model with suspended
animation 620
exercises 623
references 629
10 brownian motion and stationary processes 631
10.1 brownian motion 631
10.2 hitting times, maximum variable, and the gambler's
ruin problem 635
10.3 variations on brownian motion 636
10.3.1 brownian motion with drift 636
10.3.2 geometric brownian motion 636
10.4 pricing stock options 638
10.4.1 an example in options pricing
638
10.4.2 the arbitrage theorem 640
10.4.3 the black-scholes option pricing
formula 644
10.5 white noise 649
10.6 gaussian processes 651
10.7 stationary and weakly stationary processes
654
10.8 harmonic analysis of weakly stationary processes
659
exercises 661
references 665
11 simulation 667
11.1 introduction 667
11.2 general techniques for simulating continuous
random variables 672
11.2.1 the inverse transformation method
672
11.2.2 the rejection method 673
11.2.3 the hazard rate method 677
11.3 special techniques for simulating continuous
random variables 680
11.3.1 the normal distribution 680
11.3.2 the gamma distribution 684
11.3.3 the chi-squared distribution
684
11.3.4 the beta (n, m) distribution
685
11.3.5 the exponential distribution-the von
neumann algorithm 686
11.4 simulating from discrete distributions 688
11.4.1 the alias method 691
11.5 stochastic processes 696
11.5.1 simulating a nonhomogeneous poisson
process 697
11.5.2 simulating a two-dimensional poisson
process 703
11.6 variance reduction techniques 706
11.6.1 use of antithetic variables
707
11.6.2 variance reduction by conditioning
710
11.6.3 control variates 715
11.6.4 importance sampling 717
11.7 determining the number of runs 722
11.8 generating from the stationary distribution of a
markov chain 723
11.8.1 coupling from the past 723
11.8.2 another approach 725
exercises 726
references 734
Appendix: solutions to starred exercises 735
Index 775

章节摘录

版权页：插图：

媒体关注与评论

“本书的一大特色是实例丰富，内容涉及多个学科，尤其是精算学……相信任何有上进心的读者都会对此爱不释手。”　　——Jean LeMaire，宾夕法尼亚大学沃顿商学院“书中的例子和习题非常出色，作者不仅提供了非常基本的例子，以阐述基础概念和公式，还从尽可能多的学科中提炼出许多较高级的实例，极具参考价值。”　　——Matt Carlton，加州州立理工大学（Cal Poly）

编辑推荐

《应用随机过程:概率模型导论(英文版·第10版)》：北美精算师考试制定参考书《应用随机过程:概率模型导论(英文版·第10版)》是国际知名统计学家Sheldon M，Ross所著的关于基础概率理论和随机过程的经典教材。被加州大学伯克利分校，哥伦比亚大学、普度大学、密歇根大学、俄勒冈州立大学，华盛顿大学等众多国外知名大学所采用。与其他随机过程教材相比。《应用随机过程:概率模型导论(英文版·第10版)》非常强调实践性。内含极其丰富的例子和习题，涵盖了众多学科的各种应用。作者富于启发而又不失严密性的叙述方式，有助于使读者建立概率思维方式，培养对概率理论、随机过程的直观感觉。对那些需要将概率理论应用于精算学，运筹学，物理学，工程学，计算机科学。管理学和社会科学的读者而言，《应用随机过程:概率模型导论(英文版·第10版)》是一本极好的教材或参考书。《应用随机过程:概率模型导论(英文版·第10版)》特色秉承作者招牌式的深入浅出，娓娓道来的写作风格。增加了关于不带左跳的随机徘徊、生灭排队模型、马尔可夫链和保险破产模型等方面的重要内容。增加了新的例子和习题，更加注重强化读者的概率直观。

用户评论 (总计33条)

•   随机过程教材的经典之作，值得一看，而且要多看几遍
•   Ross的概率书都很经典，能够出10版的书肯定不一般
•   随机过程随机过。。。
•   本书浅显易懂，数学上基本上不需要复杂的工具。
•   刚刚看了两章，发现里面的例子还是不错的，喜欢。
•   例子很多，易于理解，印刷也很清晰
•   还没看内容，标题翻译的有点怪。
•   理论性强，质量很好
•   剖析比较详细
•   本学期的讨论班就用它了，不错的书
•   比较好懂的英文，不枯燥
•   算法精妙啊，快来看。
•   书完整无缺,印刷清晰
•   书还不错~虽然木有买的另一本纸质好~不是新闻纸
•   很实用，但包装有破损
•   作为一本全英文图书，我由于工作忙只看到第四章。总体感觉，本书实例确实多，作者也确实把我们当傻子教的，不厌其烦。不过也有好多地方要在网上查一些概念。推荐有自学能力的人去读。
•   10个字的规定真讨厌
•   书的上面和侧面都是脏脏的。。。哎1
•   书还不错,不过书本最后烂了几页,其他地方也是有烂的
•   Ross写书就是这个特点。清楚，例子很多
•   Ross的经典名著，内容由浅入深，例题讲解详细易懂，课后练习题很多，也有习题答案。特别适合于学习概率应用者入门！值得称道的是，这个版无论是从印刷、排版、纸张都是非常好，是我见到影印书中质量最好的，让人爱不释手啊！虽然价格也贵，但冲着作者和这么好的印刷质量，还是掏了银子拿下！
•   书是经典，质量不错，只是送货时间有点长~
•   内容很丰富，有一定难度，商品还可以，应该是正版的
•   书的质量很好内容就不用说了
•   经典书籍还用多说？偶了
•   和原版教材完全一样，很好！
•   呃，买了两本书，卓越卖的这本第二天就到了。 China-Pub那本还在等待中,已经5天了.
•   书收到还不错，网上买书就是比在书店买便宜，就是邮的太慢。
•   能出到10版的应该是经典
•   一本可以做十版的书足以见得它的经典
•   书质量看起来还好，遇到打折，还不错
•   好书！无需多说
•   暂未细读，但是翻过才买的