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by Gheorghe Oprisan, Nikolaos Limnios, Marius Iosifescu
Introduction to Stochastic Models
Cover
Dedication
Title Page
Copyright
Preface
Chapter 1: Introduction to Stochastic Processes
1.1. Sequences of random variables
1.2. The notion of stochastic process
1.3. Martingales
1.4. Markov chains
1.5. State classification
1.6. Continuous-time Markov processes
1.7. Semi-Markov processes
Chapter 2: Simple Stochastic Models
2.1. Urn models
2.2. Random walks
2.3. Brownian motion
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
3.3. Markov models in genetics
3.4. Markov storage models
3.5. Reliability of Markov 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
4.8. Alternating renewal processes
4.9. Superposition of renewal processes
4.10. Regenerative processes
Chapter 5: Semi-Markov Models
5.1. Introduction
5.2. Markov renewal processes
5.3. First-passage times and state classification
5.4. Reliability
5.5. Reservoir models
5.6. Queues
5.7. Digital communication channels
Chapter 6: Branching Models
6.1. The Bienaymé-Galton-Watson model
6.2. Generalizations of the B-G-W model
6.3. Continuous-time models
Chapter 7: Optimal Stopping Models
7.1. The classic optimal stopping problem
7.2. Renewal with binary decision
Bibliography
Notation
Index
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