An Introduction to Stochastic Modeling 3rd edition by Samuel Karlin , Howard Taylor ISBN 0126848874 978-0126848878

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ISBN 10:  0126848874 
ISBN 13: 978-0126848878
Author:Samuel Karlin , Howard M. Taylor 

“An Introduction to Stochastic Modeling” (3rd Edition) by Samuel Karlin and Howard M. Taylor is a comprehensive textbook designed to provide a detailed introduction to the theory and applications of stochastic processes. The third edition, published in 2003, continues the tradition of the earlier editions by presenting key concepts and techniques in a clear and accessible manner, while expanding on the material to reflect the advances in the field.

An Introduction to Stochastic Modeling 3rd Table of contents:

I Introduction
1. Stochastic Modeling 2. Probability Review
3. The Major Discrete Distributions
4. Important Continuous Distributions 5. Some Elementary Exercises
6. Useful Functions, Integrals, and Sums
II Conditional Probability and Conditional Expectation
1. The Discrete Case
2. The Dice Game Craps
3. Random Sums
4. Conditioning on a Continuous Random Variable 5. Martingales*
III Markov Chains: Introduction
1. Definitions
2. Transition Probability Matrices of a Markov Chain 3. Some Markov Chain Models
4. First Step Analysis
5. Some Special Markov Chains
6. Functionals of Random Walks and Success Runs
*Stars indicate topics of a more advanced or specialized nature.
7. Another Look at First Step Analysis*
8. Branching Processes*
9. Branching Processes and Generating Functions*

IV The Long Run Behavior of Markov Chains
1. Regular Transition Probability Matrices
2. Examples
3. The Classification of States
4. The Basic Limit Theorem of Markov Chains
5. Reducible Markov Chains*
V Poisson Processes
1. The Poisson Distribution and the Poisson Process 2. The Law of Rare Events
3. Distributions Associated with the Poisson Process 4. The Uniform Distribution and Poisson Processes 5. Spatial Poisson Processes
6. Compound and Marked Poisson Processes
VI Continuous Time Markov Chains
1. Pure Birth Processes
2. Pure Death Processes
3. Birth and Death Processes
4. The Limiting Behavior of Birth and Death Processes
5. Birth and Death Processes with Absorbing States

 6. Finite State Continuous Time Markov Chains

7. A Poisson Process with a Markov Intensity*
VII Renewal Phenomena
1. Definition of a Renewal Process and Related Concepts
2. Some Examples of Renewal Processes
3. The Poisson Process Viewed as a Renewal
Process

4. The Asymptotic Behavior of Renewal Processes 5. Generalizations and Variations on Renewal
Processes
6. Discrete Renewal Theory*
VIII Brownian Motion and Related Processes
1. Brownian Motion and Gaussian Processes

2. The Maximum Variable and the Reflection Principle

3. Variations and Extensions
4. Brownian Motion with Drift
5. The Ornstein-Uhlenbeck Process*
IX Queueing Systems
1. Queueing Processes
2. Poisson Arrivals, Exponential Service Times
3. General Service Time Distributions
4. Variations and Extensions
5. Open Acyclic Queueing Networks 6. General Open Networks

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Samuel Karlin,Howard Taylor,An Introduction,Stochastic Modeling