Taylor / Karlin An Introduction to Stochastic Modeling

1. Auflage 2014
ISBN: 978-1-4832-2044-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 578 Seiten, Web PDF

An Introduction to Stochastic Modeling, Revised Edition provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Autoren/Hrsg.

Taylor, Howard M.

Karlin, Samuel

Inhaltsverzeichnis

1;Front Cover;1
2;An Introduction to Stochastic Modeling;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;Chapter 1. Introduction;14
6.1;1.1 Stochastic Modeling;14
6.2;1.2 Probability Review;19
6.3;1.3 The Major Discrete Distributions;37
6.4;1.4 Important Continuous Distributions;47
6.5;1.5 Some Elementary Exercises;56
6.6;1.6 Useful Functions, Integrals, and Sums;67
7;Chapter 2. Conditional Probability and Conditional Expectation;72
7.1;2.1 The Discrete Case;72
7.2;2.2 The Dice Game Craps;79
7.3;2.3 Random Sums;84
7.4;2.4 Conditioning on a Continuous Random Variable;94
8;Chapter 3. Markov Chains: Introduction;102
8.1;3.1 Definitions;102
8.2;3.2 Transition Probability Matrices of a Markov Chain;107
8.3;3.3 Some Markov Chain Models;112
8.4;3.4 First Step Analysis;123
8.5;3.5 Some Special Markov Chains;139
8.6;3.6 Functionals of Random Walks and Success Runs;154
8.7;3.7 Another Look at First Step Analysis;171
9;Chapter 4. The Long Run Behavior of Markov Chains;180
9.1;4.1 Regular Transition Probability Matrices;180
9.2;4.2 Examples;194
9.3;4.3 The Classification of States;213
9.4;4.4 The Basic Limit Theorem of Markov Chains;225
9.5;4.5 Reducible Markov Chains;237
9.6;4.6 Sequential Decisions and Markov Chains;243
10;Chapter 5. Poisson Processes;254
10.1;5.1 The Poisson Distribution and the Poisson Process;254
10.2;5.2 The Law of Rare Events;265
10.3;5.3 Distributions Associated with the Poisson Process;274
10.4;5.4 The Uniform Distribution and Poisson Processes;282
10.5;5.5 Spatial Poisson Processes;293
10.6;5.6 Compound and Marked Poisson Processes;300
11;Chapter 6. Continuous Time Markov Chains;314
11.1;6.1 Pure Birth Processes;314
11.2;6.2 Pure Death Processes;326
11.3;6.3 Birth and Death Processes;337
11.4;6.4 The Limiting Behavior of Birth and Death Processes;345
11.5;6.5 Birth and Death Processes with Absorbing States;359
11.6;6.6 Finite State Continuous Time Markov Chains;374
11.7;6.7 Set Valued Processes;388
12;Chapter 7. Renewal Phenomena;402
12.1;7.1 Definition of a Renewal Process and Related Concepts;402
12.2;7.2 Some Examples of Renewal Processes;409
12.3;7.3 The Poisson Process Viewed as a Renewal Process;416
12.4;7.4 The Asymptotic Behavior of Renewal Processes;421
12.5;7.5 Generalizations and Variations on Renewal Processes;432
12.6;7.6 Discrete Renewal Theory;442
13;Chapter 8. Branching Processes and Population Growth;450
13.1;8.1 Branching Processes;450
13.2;8.2 Branching Processes and Generating Functions;457
13.3;8.3 Geometrically Distributed Offspring;467
13.4;8.4 Variations on Branching Processes;474
13.5;8.5 Some Stochastic Models of Plasmid Reproduction and Plasmid Copy Number Partition;480
13.6;8.6 Population Growth Processes with Interacting Types;485
13.7;8.7 Deterministic Population Growth with Age Distribution;487
14;Chapter 9. Queueing Systems;498
14.1;9.1 Queueing Processes;498
14.2;9.2 Poisson Arrivals and Exponentially Distributed Service Times;503
14.3;9.3 The /W/G/1 and M/G/8 Systems ;514
14.4;9.4 Variations and Extensions;523
14.5;9.5 Open Acyclic Queueing Networks;536
14.6;9.6 General Open Networks;547
15;Further Readings;556
16;Solutions to Selected Exercises;558
17;Index;576