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Edition: 3RD 98

Copyright: 1998

Publisher: Academic Press, Inc.

Published: 1998

International: No

Copyright: 1998

Publisher: Academic Press, Inc.

Published: 1998

International: No

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*An Introduction to Stochastic Modeling*, Third Edition serves as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus. It bridges the gap between basic probability know-how and an intermediate level course in stochastic processes. The objectives of the book 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.

Realistic applications from a variety of disciplines integrated throughout the book

New chapter on Brownian motion and related processes

Additional sections on Martingales and Poisson process

Updated and more rigorous problems, including computer "challenges"

Revised end-of-chapter exercise sets

**Introduction **

Stochastic Modeling.

Probability Review.

The Major Discrete Distributions.

Important Continuous Distributions.

Some Elementary Exercises.

Useful Functions, Integrals, and Sums.

**Conditional Probability and Conditional Expectation **

The Discrete Case.

The Dice Game Craps.

Random Sums.

Conditioning on a Continuous Random Variable.

Martingales.

**Markov Chains: Introduction **

Definitions.

Transition Probability Matrices of a Markov Chain.

Some Markov Chain Models.

First Step Analysis.

Some Special Markov Chains.

Functionals of Random Walks and Success Runs.

Another Look at First Step Analysis.

Branching Processes.

Branching Processes and Generating Functions.

**The Long Run Behavior of Markov Chains**

Regular Transition Probability Matrices.

Examples.

The Classification of States.

The Basic Limit Theorem of Markov Chains.

Reducible Markov Chains.

**Poisson Processes**

The Poisson Distribution and the Poisson Processes.

The Law of Rare Events.

Distributions Associated with the Poisson Process.

The Uniform Distribution and Poisson Processes.

Spatial Poisson Processes.

Compound and Marked Poisson Processes.

**Continuous Time Markov Chains **

Pure Birth Processes.

Pure Death Processes.

Birth and Death Processes.

The Limiting Behavior of Birth and Death Processes.

Birth and Death Processes with Absorbing States.

Finite State Continuous Time Markov Chains.

A Poisson Process with a Markov Intensity.

**Renewal Phenomena **

Definition of a Renewal Process and Related Concepts.

Some Examples of Renewal Processes.

The Poisson Process Viewed as a Renewal Process.

The Asymptotic Behavior of Renewal Processes.

Generalizations and Variations on Renewal Processes.

Discrete Renewal Theory.

**Brownian Motion and Related Processes **

Brownian Motion and Gaussian Processes.

The Maximum Variable and the Reflection Principle.

Variations and Extensions.

Brownian Motion with Drift.

The Ornstein-Uhlenbeck Process.

**Queueing Systems **

Queueing Processes.

Poisson Arrivals, Exponential Service Times.

General Service Time Distributions.

Variations and Extensions.

Open Acylclic Queueing Networks.

General Open Networks.

Further Readings.

Answers to Exercises.

Subject Index.

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Summary

*An Introduction to Stochastic Modeling*, Third Edition serves as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus. It bridges the gap between basic probability know-how and an intermediate level course in stochastic processes. The objectives of the book 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.

Realistic applications from a variety of disciplines integrated throughout the book

New chapter on Brownian motion and related processes

Additional sections on Martingales and Poisson process

Updated and more rigorous problems, including computer "challenges"

Revised end-of-chapter exercise sets

Table of Contents

**Introduction **

Stochastic Modeling.

Probability Review.

The Major Discrete Distributions.

Important Continuous Distributions.

Some Elementary Exercises.

Useful Functions, Integrals, and Sums.

**Conditional Probability and Conditional Expectation **

The Discrete Case.

The Dice Game Craps.

Random Sums.

Conditioning on a Continuous Random Variable.

Martingales.

**Markov Chains: Introduction **

Definitions.

Transition Probability Matrices of a Markov Chain.

Some Markov Chain Models.

First Step Analysis.

Some Special Markov Chains.

Functionals of Random Walks and Success Runs.

Another Look at First Step Analysis.

Branching Processes.

Branching Processes and Generating Functions.

**The Long Run Behavior of Markov Chains**

Regular Transition Probability Matrices.

Examples.

The Classification of States.

The Basic Limit Theorem of Markov Chains.

Reducible Markov Chains.

**Poisson Processes**

The Poisson Distribution and the Poisson Processes.

The Law of Rare Events.

Distributions Associated with the Poisson Process.

The Uniform Distribution and Poisson Processes.

Spatial Poisson Processes.

Compound and Marked Poisson Processes.

**Continuous Time Markov Chains **

Pure Birth Processes.

Pure Death Processes.

Birth and Death Processes.

The Limiting Behavior of Birth and Death Processes.

Birth and Death Processes with Absorbing States.

Finite State Continuous Time Markov Chains.

A Poisson Process with a Markov Intensity.

**Renewal Phenomena **

Definition of a Renewal Process and Related Concepts.

Some Examples of Renewal Processes.

The Poisson Process Viewed as a Renewal Process.

The Asymptotic Behavior of Renewal Processes.

Generalizations and Variations on Renewal Processes.

Discrete Renewal Theory.

**Brownian Motion and Related Processes **

Brownian Motion and Gaussian Processes.

The Maximum Variable and the Reflection Principle.

Variations and Extensions.

Brownian Motion with Drift.

The Ornstein-Uhlenbeck Process.

**Queueing Systems **

Queueing Processes.

Poisson Arrivals, Exponential Service Times.

General Service Time Distributions.

Variations and Extensions.

Open Acylclic Queueing Networks.

General Open Networks.

Further Readings.

Answers to Exercises.

Subject Index.

Publisher Info

Publisher: Academic Press, Inc.

Published: 1998

International: No

Published: 1998

International: No

*An Introduction to Stochastic Modeling*, Third Edition serves as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus. It bridges the gap between basic probability know-how and an intermediate level course in stochastic processes. The objectives of the book 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.

Realistic applications from a variety of disciplines integrated throughout the book

New chapter on Brownian motion and related processes

Additional sections on Martingales and Poisson process

Updated and more rigorous problems, including computer "challenges"

Revised end-of-chapter exercise sets

**Introduction **

Stochastic Modeling.

Probability Review.

The Major Discrete Distributions.

Important Continuous Distributions.

Some Elementary Exercises.

Useful Functions, Integrals, and Sums.

**Conditional Probability and Conditional Expectation **

The Discrete Case.

The Dice Game Craps.

Random Sums.

Conditioning on a Continuous Random Variable.

Martingales.

**Markov Chains: Introduction **

Definitions.

Transition Probability Matrices of a Markov Chain.

Some Markov Chain Models.

First Step Analysis.

Some Special Markov Chains.

Functionals of Random Walks and Success Runs.

Another Look at First Step Analysis.

Branching Processes.

Branching Processes and Generating Functions.

**The Long Run Behavior of Markov Chains**

Regular Transition Probability Matrices.

Examples.

The Classification of States.

The Basic Limit Theorem of Markov Chains.

Reducible Markov Chains.

**Poisson Processes**

The Poisson Distribution and the Poisson Processes.

The Law of Rare Events.

Distributions Associated with the Poisson Process.

The Uniform Distribution and Poisson Processes.

Spatial Poisson Processes.

Compound and Marked Poisson Processes.

**Continuous Time Markov Chains **

Pure Birth Processes.

Pure Death Processes.

Birth and Death Processes.

The Limiting Behavior of Birth and Death Processes.

Birth and Death Processes with Absorbing States.

Finite State Continuous Time Markov Chains.

A Poisson Process with a Markov Intensity.

**Renewal Phenomena **

Definition of a Renewal Process and Related Concepts.

Some Examples of Renewal Processes.

The Poisson Process Viewed as a Renewal Process.

The Asymptotic Behavior of Renewal Processes.

Generalizations and Variations on Renewal Processes.

Discrete Renewal Theory.

**Brownian Motion and Related Processes **

Brownian Motion and Gaussian Processes.

The Maximum Variable and the Reflection Principle.

Variations and Extensions.

Brownian Motion with Drift.

The Ornstein-Uhlenbeck Process.

**Queueing Systems **

Queueing Processes.

Poisson Arrivals, Exponential Service Times.

General Service Time Distributions.

Variations and Extensions.

Open Acylclic Queueing Networks.

General Open Networks.

Further Readings.

Answers to Exercises.

Subject Index.