Probability and random processes / G.R. Grimmett, D.R. Stirzaker.
Editor: Oxford : New York : Clarendon Press ; Oxford University Press, c1992Edición: 2nd edDescripción: xii, 541 p. : ill. ; 24 cmISBN: 0198536666 :; 0198536658 (pbk.) :Tema(s): Probabilities | Stochastic processesOtra clasificación: *CODIGO* Recursos en línea: Publisher description | Table of contents only1 1.1 Events and their probabilities Introduction1 1.2 Events as sets [1] 1.3 Probability [4] 1.4 Conditional probability: a fundamental lemma [8] 1.5 Independence [13] 1.6 Completeness and product spaces [14] 1.7 Worked examples [16] 1.8 Problems [21] 2 Random variables and their distributions 2.1 Random variables [25] 2.2 The law of averages [29] 2.3 Discrete and continuous variables [32] 2.4 Worked examples [35] 2.5 Random vectors [38] 2.6 Monte Carlo simulation [41] 2.7 Problems [43] 3 Discrete random variables 3.1 Probability mass functions [46] 3.2 Independence [47] 3.3 Expectation [50] 3.4 Indicators and matching [56] 3.5 Examples of discrete variables [60] 3.6 Dependence [62] 3.7 Conditional distributions and conditional expectation [67] 3.8 Sums of random variables [70] 3.9 Simple random walk [71] 3.10 Random walk: counting sample paths [75] 3.11 Problems [83] 4 Continuous random variables 4.1 Probability density functions [89] 4.2 Independence [91] 4.3 Expectation [92] 4.4 Examples of continuous variables [94] 4.5 Dependence [98] 4.6 Conditional distributions and conditional expectation [103] 4.7 Functions of random variables [107] 4.8 Sums of random variables [113] 4.9 Multivariate normal distribution [114] 4.10 Distributions arising from the normal distribution [118] 4.11 Problems [121] 5 5.1Generating functions and their applications Generating functions [127] 5.2 Some applications [135] 5.3 Random walk [141] 5.4 Branching processes [150] 5.5 Age-dependent branching processes [155] 5.6 Expectation revisited [158] 5.7 Characteristic functions [162] 5.8 Examples of characteristic functions [167] 5.9 Inversion and continuity theorems [170] 5.10 Two limit theorems [174] 5.11 Large deviations [183] 5.12 Problems [187] 6 Markov chains 6.1 Markov processes [194] 6.2 Classification of states [201] 6.3 Classification of chains [204] 6.4 Stationary distributions and the limit theorem [207] 6.5 Time-reversibility [218] 6.6 Chains with finitely many states [221] 6.7 Branching processes revisited [224] 6.8 Birth processes and the Poisson process [228] 6.9 Continuous-time Markov chains [239] 6.10 Uniform semigroups [246] 6.11 Birth-death processes and imbedding [249] 6.12 Special processes [256] 6.13 Problems [264] 7 Convergence of random variables 7.1 Introduction [271] 7.2 Modes of convergence [274] 7.3 Some ancillary results [285] 7.4 Laws of large numbers [293] 7.5 The strong law [297] 7.6 The law of the iterated logarithm [301] 7.7 Martingales [302] 7.8 Martingale convergence theorem [309] 7.9 Prediction and conditional expectation [314] 7.10 Uniform integrability [322] 7.11 Problems [326] 8 Random processes 8.1 Introduction [332] 8.2 Stationary processes [333] 8 3 Renewal processes [337] 8.4 Queues [340] 8.5 The Wiener process [342] 8.6 What is in a name? [343] 8.7 Problems [346] 9 Stationary processes 9.1 Introduction [347] 9.2 Linear prediction [349] 9.3 Autocovariances and spectra [352] 9.4 Stochastic integration and the spectral representation [360] 9.5 The ergodic theorem [367] 9.6 Gaussian processes [380] 9.7 Problems [384] 10 Renewals 10.1 The renewal equation [388] 10.2 Limit theorems [393] 10.3 Excess life [398] 10.4 Applications [401] 10.5 Problems [410] 11 Queues 11.1 Single-server queues [414] 11.2 M/M/1 [416] 11.3 M/G/1 [420] 11.4 G/M/1 [427] 11.5 G/G/1 [431] 11.6 Heavy traffic [438] 11.7 Problems [439] 12 Martingales 12.1 Introduction [443] 12.2 Martingale differences and Hoeffding’s inequality [448] 12.3 Crossings and convergence [453] 12.4 Stopping times [459] 12.5 Optional stopping [464] 12.6 The maximal inequality [469] 12.7 Backward martingales and continuous-time martingales [472] 12.8 Some examples [477] 12.9 Problems [482] 13 Diffusion processes 13.1 Introduction [487] 13.2 Brownian motion [487] 13.3 Diffusion processes [490] 13.4 First passage times [500] 13.5 Barriers [505] 13.6 Excursions, and the Brownian bridge [509] 13,7 Potential theory [512] 13.8 Problems [518] Appendix 1. Foundations and notation [521] Appendix II. Further reading [526] Appendix III. History and varieties of probability [527] Appendix IV. John Arbuthnot's Preface to Of the laws of chance (1692) [529] Bibliography [532] List of notation [534] Index [535]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 60 G864-2 (Browse shelf) | Available | A-9338 |
Includes bibliographical references (p.[532]-533) and index.
1 1.1 Events and their probabilities Introduction1 --
1.2 Events as sets [1] --
1.3 Probability [4] --
1.4 Conditional probability: a fundamental lemma [8] --
1.5 Independence [13] --
1.6 Completeness and product spaces [14] --
1.7 Worked examples [16] --
1.8 Problems [21] --
2 Random variables and their distributions --
2.1 Random variables [25] --
2.2 The law of averages [29] --
2.3 Discrete and continuous variables [32] --
2.4 Worked examples [35] --
2.5 Random vectors [38] --
2.6 Monte Carlo simulation [41] --
2.7 Problems [43] --
3 Discrete random variables --
3.1 Probability mass functions [46] --
3.2 Independence [47] --
3.3 Expectation [50] --
3.4 Indicators and matching [56] --
3.5 Examples of discrete variables [60] --
3.6 Dependence [62] --
3.7 Conditional distributions and conditional expectation [67] --
3.8 Sums of random variables [70] --
3.9 Simple random walk [71] --
3.10 Random walk: counting sample paths [75] --
3.11 Problems [83] --
4 Continuous random variables --
4.1 Probability density functions [89] --
4.2 Independence [91] --
4.3 Expectation [92] --
4.4 Examples of continuous variables [94] --
4.5 Dependence [98] --
4.6 Conditional distributions and conditional expectation [103] --
4.7 Functions of random variables [107] --
4.8 Sums of random variables [113] --
4.9 Multivariate normal distribution [114] --
4.10 Distributions arising from the normal distribution [118] --
4.11 Problems [121] --
5 5.1Generating functions and their applications Generating functions [127] --
5.2 Some applications [135] --
5.3 Random walk [141] --
5.4 Branching processes [150] --
5.5 Age-dependent branching processes [155] --
5.6 Expectation revisited [158] --
5.7 Characteristic functions [162] --
5.8 Examples of characteristic functions [167] --
5.9 Inversion and continuity theorems [170] --
5.10 Two limit theorems [174] --
5.11 Large deviations [183] --
5.12 Problems [187] --
6 Markov chains --
6.1 Markov processes [194] --
6.2 Classification of states [201] --
6.3 Classification of chains [204] --
6.4 Stationary distributions and the limit theorem [207] --
6.5 Time-reversibility [218] --
6.6 Chains with finitely many states [221] --
6.7 Branching processes revisited [224] --
6.8 Birth processes and the Poisson process [228] --
6.9 Continuous-time Markov chains [239] --
6.10 Uniform semigroups [246] --
6.11 Birth-death processes and imbedding [249] --
6.12 Special processes [256] --
6.13 Problems [264] --
7 Convergence of random variables --
7.1 Introduction [271] --
7.2 Modes of convergence [274] --
7.3 Some ancillary results [285] --
7.4 Laws of large numbers [293] --
7.5 The strong law [297] --
7.6 The law of the iterated logarithm [301] --
7.7 Martingales [302] --
7.8 Martingale convergence theorem [309] --
7.9 Prediction and conditional expectation [314] --
7.10 Uniform integrability [322] --
7.11 Problems [326] --
8 Random processes --
8.1 Introduction [332] --
8.2 Stationary processes [333] --
8 3 Renewal processes [337] --
8.4 Queues [340] --
8.5 The Wiener process [342] --
8.6 What is in a name? [343] --
8.7 Problems [346] --
9 Stationary processes --
9.1 Introduction [347] --
9.2 Linear prediction [349] --
9.3 Autocovariances and spectra [352] --
9.4 Stochastic integration and the spectral representation [360] --
9.5 The ergodic theorem [367] --
9.6 Gaussian processes [380] --
9.7 Problems [384] --
10 Renewals --
10.1 The renewal equation [388] --
10.2 Limit theorems [393] --
10.3 Excess life [398] --
10.4 Applications [401] --
10.5 Problems [410] --
11 Queues --
11.1 Single-server queues [414] --
11.2 M/M/1 [416] --
11.3 M/G/1 [420] --
11.4 G/M/1 [427] --
11.5 G/G/1 [431] --
11.6 Heavy traffic [438] --
11.7 Problems [439] --
12 Martingales --
12.1 Introduction [443] --
12.2 Martingale differences and Hoeffding’s inequality [448] --
12.3 Crossings and convergence [453] --
12.4 Stopping times [459] --
12.5 Optional stopping [464] --
12.6 The maximal inequality [469] --
12.7 Backward martingales and continuous-time martingales [472] --
12.8 Some examples [477] --
12.9 Problems [482] --
13 Diffusion processes --
13.1 Introduction [487] --
13.2 Brownian motion [487] --
13.3 Diffusion processes [490] --
13.4 First passage times [500] --
13.5 Barriers [505] --
13.6 Excursions, and the Brownian bridge [509] --
13,7 Potential theory [512] --
13.8 Problems [518] --
Appendix 1. Foundations and notation [521] --
Appendix II. Further reading [526] --
Appendix III. History and varieties of probability [527] --
Appendix IV. John Arbuthnot's Preface to Of the laws of chance (1692) [529] --
Bibliography [532] --
List of notation [534] --
Index [535] --
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