An Introduction to Stochastic Modeling 4th Edition by Mark Pinsky, Samuel Karlin – Ebook PDF Instant Download/Delivery: 0123814162, 978-0123814166
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ISBN 10: 0123814162
ISBN 13: 978-0123814166
Author: Mark Pinsky, Samuel Karlin
Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, the fourth edition of Introduction to Stochastic Modeling bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems.
An Introduction to Stochastic Modeling 4th Table of contents:
Chapter 1. Introduction
1.1. Stochastic Modeling
1.2. Probability Review
1.3. The Major Discrete Distributions
1.4. Important Continuous Distributions
1.5. Some Elementary Exercises
1.6. Useful Functions, Integrals, and Sums
Chapter 2. Conditional Probability and Conditional Expectation
2.1. The Discrete Case
2.2. The Dice Game Craps
2.3. Random Sums
2.4. Conditioning on a Continuous Random Variable
2.5. Martingales
Chapter 3. Markov Chains: Introduction
3.1. Definitions
3.2. Transition Probability Matrices of a Markov Chain
3.3. Some Markov Chain Models
3.4. First Step Analysis
3.5. Some Special Markov Chains
3.6. Functionals of Random Walks and Success Runs
3.7. Another Look at First Step Analysis
3.8. Branching Processes
3.9. Branching Processes and Generating Functions
Chapter 4. The Long Run Behavior of Markov Chains
4.1. Regular Transition Probability Matrices
4.2. Examples
4.3. The Classification of States
4.4. The Basic Limit Theorem of Markov Chains
4.5. Reducible Markov Chains
Chapter 5. Poisson Processes
5.1. The Poisson Distribution and the Poisson Process
5.2. The Law of Rare Events
5.3. Distributions Associated with the Poisson Process
5.4. The Uniform Distribution and Poisson Processes
5.5. Spatial Poisson Processes
5.6. Compound and Marked Poisson Processes
Chapter 6. Continuous Time Markov Chains
6.1. Pure Birth Processes
6.2. Pure Death Processes
6.3. Birth and Death Processes
6.4. The Limiting Behavior of Birth and Death Processes
6.5. Birth and Death Processes with Absorbing States
6.6. Finite-State Continuous Time Markov Chains
6.7. A Poisson Process with a Markov Intensity
Chapter 7. Renewal Phenomena
7.1. Definition of a Renewal Process and Related Concepts
7.2. Some Examples of Renewal Processes
7.3. The Poisson Process Viewed as a Renewal Process
7.4. The Asymptotic Behavior of Renewal Processes
7.5. Generalizations and Variations on Renewal Processes
7.6. Discrete Renewal Theory
Chapter 8. Brownian Motion and Related Processes
8.1. Brownian Motion and Gaussian Processes
8.2. The Maximum Variable and the Reflection Principle
8.3. Variations and Extensions
8.4. Brownian Motion with Drift
8.5. The Ornstein–Uhlenbeck Process
Chapter 9. Queueing Systems
9.1. Queueing Processes
9.2. Poisson Arrivals, Exponential Service Times
9.3. General Service Time Distributions
9.4. Variations and Extensions
9.5. Open Acyclic Queueing Networks
9.6. General Open Networks
Chapter 10. Random Evolutions
10.1. Two-State Velocity Model
10.2. N-State Random Evolution
10.3. Weak Law and Central Limit Theorem
10.4. Isotropic Transport in Higher Dimensions
Chapter 11. Characteristic Functions and Their Applications
11.1. Definition of the Characteristic Function
11.2. Inversion Formulas for Characteristic Functions
11.3. Inversion Formula for General Random Variables
11.4. The Continuity Theorem
11.5. Proof of the Central Limit Theorem
11.6. Stirling’s Formula and Applications
11.7. Local deMoivre–Laplace Theorem
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