Introduction to Probability Models

Höfundur: Sheldon M. Ross (Útgáfa: 13)
Introduction to Probability Models

Kaup valmöguleikar

Introduction to Probability Models: Thirteenth Edition is available in two manageable volumes: an Elementary edition appropriate for undergraduate use and an Advanced edition for graduate use. Together, and through their hallmark exercises and real examples, both versions offer a comprehensive foundation of this key subject with applications across engineering, computer science, management science, the physical and social sciences and operations research.

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Útgefandi
Elsevier S & T
ISBN
9780443187605
Print ISBN
9780443187612
Format
ePub
Útgáfa
13
Höfundar
Sheldon M. Ross
Tungumál
English
Útgefið
2023-06-30
Prent takmörkun á líftíma
10

Kaflar

  • Title of Book
  • Cover image
  • Title page
  • Table of Contents
  • Copyright
  • Preface
  • New to This Edition
  • Course
  • Examples and Exercises
  • Organization
  • Acknowledgments
  • 1. Introduction to Probability Theory
  • Abstract
  • 1.1 Introduction
  • 1.2 Sample Space and Events
  • 1.3 Probabilities Defined on Events
  • 1.4 Conditional Probabilities
  • 1.5 Independent Events
  • 1.6 Bayes' Formula
  • 1.7 Probability Is a Continuous Event Function
  • Exercises
  • References
  • 2. Random Variables
  • Abstract
  • 2.1 Random Variables
  • 2.2 Discrete Random Variables
  • 2.3 Continuous Random Variables
  • 2.4 Expectation of a Random Variable
  • 2.5 Jointly Distributed Random Variables
  • 2.6 Moment Generating Functions
  • 2.7 Limit Theorems
  • 2.8 Proof of the Strong Law of Large Numbers
  • 2.9 Stochastic Processes
  • Exercises
  • References
  • 3. Conditional Probability and Conditional Expectation
  • Abstract
  • 3.1 Introduction
  • 3.2 The Discrete Case
  • 3.3 The Continuous Case
  • 3.4 Computing Expectations by Conditioning
  • 3.5 Computing Probabilities by Conditioning
  • 3.6 Some Applications
  • 3.7 An Identity for Compound Random Variables
  • Exercises
  • 4. Markov Chains
  • Abstract
  • 4.1 Introduction
  • 4.2 Chapman–Kolmogorov Equations
  • 4.3 Classification of States
  • 4.4 Long-Run Proportions and Limiting Probabilities
  • 4.5 Some Applications
  • 4.6 Mean Time Spent in Transient States
  • 4.7 Branching Processes
  • 4.8 Time Reversible Markov Chains
  • 4.9 Markov Chain Monte Carlo Methods
  • 4.10 Markov Decision Processes
  • 4.11 Hidden Markov Chains
  • Exercises
  • References
  • 5. The Exponential Distribution and the Poisson Process
  • Abstract
  • 5.1 Introduction
  • 5.2 The Exponential Distribution
  • 5.3 The Poisson Process
  • 5.4 Generalizations of the Poisson Process
  • 5.5 Random Intensity Functions and Hawkes Processes
  • Exercises
  • References
  • 6. Continuous-Time Markov Chains
  • Abstract
  • 6.1 Introduction
  • 6.2 Continuous-Time Markov Chains
  • 6.3 Birth and Death Processes
  • 6.4 The Transition Probability Function Pij(t)Pij(t)
  • 6.5 Limiting Probabilities
  • 6.6 Time Reversibility
  • 6.7 The Reversed Chain
  • 6.8 Uniformization
  • 6.9 Computing the Transition Probabilities
  • Exercises
  • References
  • 7. Renewal Theory and Its Applications
  • Abstract
  • 7.1 Introduction
  • 7.2 Distribution of N(t)N(t)
  • 7.3 Limit Theorems and Their Applications
  • 7.4 Renewal Reward Processes
  • 7.5 Regenerative Processes
  • 7.6 Semi-Markov Processes
  • 7.7 The Inspection Paradox
  • 7.8 Computing the Renewal Function
  • 7.9 Applications to Patterns
  • 7.10 The Insurance Ruin Problem
  • Exercises
  • References
  • 8. Queueing Theory
  • Abstract
  • 8.1 Introduction
  • 8.2 Preliminaries
  • 8.3 Exponential Models
  • 8.4 Network of Queues
  • 8.5 The System M/G/1M/G/1
  • 8.6 Variations on the M/G/1M/G/1
  • 8.7 The Model G/M/1G/M/1
  • 8.8 A Finite Source Model
  • 8.9 Multiserver Queues
  • Exercises
  • 9. Reliability Theory
  • Abstract
  • 9.1 Introduction
  • 9.2 Structure Functions
  • 9.3 Reliability of Systems of Independent Components
  • 9.4 Bounds on the Reliability Function
  • 9.5 System Life as a Function of Component Lives
  • 9.6 Expected System Lifetime
  • 9.7 Systems with Repair
  • Exercises
  • References
  • 10. Brownian Motion and Stationary Processes
  • Abstract
  • 10.1 Brownian Motion
  • 10.2 Hitting Times, Maximum Variable, and the Gambler's Ruin Problem
  • 10.3 Variations on Brownian Motion
  • 10.4 Pricing Stock Options
  • 10.5 The Maximum of Brownian Motion with Drift
  • 10.6 White Noise
  • 10.7 Gaussian Processes
  • 10.8 Stationary and Weakly Stationary Processes
  • 10.9 Harmonic Analysis of Weakly Stationary Processes
  • Exercises
  • References
  • 11. Simulation
  • Abstract
  • 11.1 Introduction
  • 11.2 General Techniques for Simulating Continuous Random Variables
  • 11.3 Special Techniques for Simulating Continuous Random Variables
  • 11.4 Simulating from Discrete Distributions
  • 11.5 Stochastic Processes
  • 11.6 Variance Reduction Techniques
  • 11.7 Determining the Number of Runs
  • 11.8 Generating from the Stationary Distribution of a Markov Chain
  • Exercises
  • References
  • 12. Coupling
  • Abstract
  • 12.1 A Brief Introduction
  • 12.2 Coupling and Stochastic Order Relations
  • 12.3 Stochastic Ordering of Stochastic Processes
  • 12.4 Maximum Couplings, Total Variation Distance, and the Coupling Identity
  • 12.5 Applications of the Coupling Identity
  • 12.6 Coupling and Stochastic Optimization
  • 12.7 Chen–Stein Poisson Approximation Bounds
  • Exercises
  • 13. Martingales
  • Abstract
  • 13.1 Introduction
  • 13.2 The Martingale Stopping Theorem
  • 13.3 Applications of the Martingale Stopping Theorem
  • 13.4 Submartingales
  • Exercises
  • Solutions to Starred Exercises
  • Chapter 1
  • Chapter 2
  • Chapter 3
  • Chapter 4
  • Chapter 5
  • Chapter 6
  • Chapter 7
  • Chapter 8
  • Chapter 9
  • Chapter 10
  • Chapter 11
  • Index