應用隨機過程

內(nèi)容概要

《應用隨機過程:概率模型導論(英文版·第10版)》由Sheldon
M.Ross所著，敘述深入淺出，涉及面廣。主要內(nèi)容有隨機變量、條件概率及條件期望、離散及連續(xù)馬爾可夫鏈、指數(shù)分布、泊松過程、布朗運動及平穩(wěn)過程、更新理論及排隊論等；也包括了隨機過程在物理、生物、運籌、網(wǎng)絡、遺傳、經(jīng)濟、保險、金融及可靠性中的應用。特別是有關隨機模擬的內(nèi)容，給隨機系統(tǒng)運行的模擬計算提供了有力的工具。除正文外，《應用隨機過程——概率模型導論(第10版:英文版)》有約700道習題，其中帶星號的習題還提供了解答。
《應用隨機過程:概率模型導論(英文版·第10版)》可作為概率論與統(tǒng)計、計算機科學、保險學、物理學、社會科學、生命科學、管理科學與工程學等專業(yè)的隨機過程基礎課教材。

作者簡介

羅斯，Sheldon
M.Ross國際知名概率與統(tǒng)計學家，南加州大學工業(yè)工程與運籌系系主任。1968年博士畢業(yè)于斯坦福大學統(tǒng)計系，曾在加州大學伯克利分校任教多年。研究領域包括：隨機模型．仿真模擬、統(tǒng)計分析、金融數(shù)學等：Ross教授著述頗豐，他的多種暢銷數(shù)學和統(tǒng)計教材均產(chǎn)生了世界性的影響，如Simulation(《統(tǒng)計模擬》)、Introduction
to Probability Models(《應用隨機過程：概率模型導論》)等（均由人民郵電出版社出版）。

書籍目錄

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

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媒體關注與評論

“本書的一大特色是實例豐富，內(nèi)容涉及多個學科，尤其是精算學……相信任何有上進心的讀者都會對此愛不釋手?！薄　　狫ean LeMaire，賓夕法尼亞大學沃頓商學院“書中的例子和習題非常出色，作者不僅提供了非常基本的例子，以闡述基礎概念和公式，還從盡可能多的學科中提煉出許多較高級的實例，極具參考價值?！薄　　狹att Carlton，加州州立理工大學（Cal Poly）

編輯推薦

《應用隨機過程:概率模型導論(英文版·第10版)》：北美精算師考試制定參考書《應用隨機過程:概率模型導論(英文版·第10版)》是國際知名統(tǒng)計學家Sheldon M，Ross所著的關于基礎概率理論和隨機過程的經(jīng)典教材。被加州大學伯克利分校，哥倫比亞大學、普度大學、密歇根大學、俄勒岡州立大學，華盛頓大學等眾多國外知名大學所采用。與其他隨機過程教材相比?！稇秒S機過程:概率模型導論(英文版·第10版)》非常強調(diào)實踐性。內(nèi)含極其豐富的例子和習題，涵蓋了眾多學科的各種應用。作者富于啟發(fā)而又不失嚴密性的敘述方式，有助于使讀者建立概率思維方式，培養(yǎng)對概率理論、隨機過程的直觀感覺。對那些需要將概率理論應用于精算學，運籌學，物理學，工程學，計算機科學。管理學和社會科學的讀者而言，《應用隨機過程:概率模型導論(英文版·第10版)》是一本極好的教材或參考書?！稇秒S機過程:概率模型導論(英文版·第10版)》特色秉承作者招牌式的深入淺出，娓娓道來的寫作風格。增加了關于不帶左跳的隨機徘徊、生滅排隊模型、馬爾可夫鏈和保險破產(chǎn)模型等方面的重要內(nèi)容。增加了新的例子和習題，更加注重強化讀者的概率直觀。

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