| Description |
1 online resource (xi, 371 pages) : illustrations |
| Series |
Applied stochastic methods series |
|
Applied stochastic methods series.
|
| Bibliography |
Includes bibliographical references and index. |
| Contents |
Cover; Introduction to Stochastic Models; Title Page; Copyright Page; Table of Contents; Preface; Chapter 1. Introduction to Stochastic Processes; 1.1. Sequences of random variables; 1.2. The notion of stochastic process; 1.3. Martingales; 1.3.1. Stopping time; 1.3.2. Discrete-time martingales; 1.3.3. Martingale convergence; 1.3.4. Square integrable martingales; 1.4. Markov chains; 1.4.1. Markov property; 1.4.2. Transition function; 1.4.3. Strong Markov property; 1.5. State classification; 1.5.1. Stationary probability; 1.6. Continuous-time Markov processes; 1.6.1. Transition function |
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1.6.2. Kolmogorov equations1.7. Semi-Markov processes; 1.7.1. Markov renewal processes; 1.7.2. Semi-Markov processes; Chapter 2. Simple Stochastic Models; 2.1. Urn models; 2.2. Random walks; 2.3. Brownian motion; 2.3.1. Introduction; 2.3.2. Basic properties; 2.4. Poisson processes; 2.5. Birth and death processes; Chapter 3. Elements of Markov Modeling; 3.1. Markov models: ideas, history, applications; 3.2. The discrete-time Ehrenfest model; 3.2.1. The microscopic chain; 3.2.2. The macroscopic chain; 3.2.3. Some characteristics of the Ehrenfest model |
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3.2.4. The discrete-time Ehrenfest model: history, generalizations, similar models3.3. Markov models in genetics; 3.3.1. Laws of heredity and mathematics; 3.3.2. Haploid models; 3.3.3. Models with two genotypes and without mutations; 3.3.4. Models with several genotypes and without mutations; 3.3.5. Models with two genotypes and mutations; 3.3.6. Models with several genotypes and mutations; 3.3.7. Models with partitioned population; 3.3.8. Genealogy models for large size populations; 3.4. Markov storage models; 3.4.1. Discrete-time models; 3.4.2. Continuous-time models |
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3.4.3. A generalized storage model3.5. Reliability of Markov models; 3.5.1. Introduction to reliability; 3.5.2. Some classes of survival distributions; 3.5.3. Discrete-time models; 3.5.4. Continuous-time models; Chapter 4. Renewal Models; 4.1. Fundamental concepts and examples; 4.2. Waiting times; 4.3. Modified renewal processes; 4.4. Replacement models; 4.5. Renewal reward processes; 4.6. The risk problem of an insurance company; 4.7. Counter models; 4.7.1. Type I counters; 4.7.2. Type II counters; 4.8. Alternating renewal processes; 4.9. Superposition of renewal processes |
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4.10. Regenerative processesChapter 5. Semi-Markov Models; 5.1. Introduction; 5.2. Markov renewal processes; 5.2.1. Definitions; 5.2.2. Markov renewal theory; 5.3. First-passage times and state classification; 5.3.1. Stationary distribution and asymptotic results; 5.4. Reliability; 5.5. Reservoir models; 5.5.1. Model I; 5.5.2. Model II; 5.6. Queues; 5.6.1. The G/M/1 queue; 5.6.2. The M/G/1 queue; 5.7. Digital communication channels; Chapter 6. Branching Models; 6.1. The Bienaymé-Galton-Watson model; 6.1.1. Historical considerations; 6.1.2. Some elementary results; 6.1.3. A fundamental example |
| Summary |
This book provides a pedagogical examination of the way in which stochastic models are encountered in applied sciences and techniques such as physics, engineering, biology and genetics, economics and social sciences. It covers Markov and semi-Markov models, as well as their particular cases: Poisson, renewal processes, branching processes, Ehrenfest models, genetic models, optimal stopping, reliability, reservoir theory, storage models, and queuing systems. Given this comprehensive treatment of the subject, students and researchers in applied sciences, as well as anyone looking for an introduc. |
| Subject |
Stochastic processes.
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Stochastic models.
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Stochastic Processes |
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Processus stochastiques. |
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Modèles stochastiques. |
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Stochastic models |
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Stochastic processes |
| Added Author |
Limnios, N. (Nikolaos)
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|
Oprișan, Gheorghe.
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| Other Form: |
Print version: 9781848210578 1848210574 (DLC) 2009051756 |
| ISBN |
0470394072 (electronic bk.) |
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9780470394076 (electronic bk.) |
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9781118623220 (electronic bk.) |
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1118623223 (electronic bk.) |
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9781118623527 |
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1118623525 |
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