Introduction to Stochastic Processes 1st Edition by Paul Gerhard Hoel, Sidney Port, Charles Stone ISBN 1478616997 9781478616993

Introduction to Stochastic Processes 1st Edition by Paul Gerhard Hoel, Sidney C. Port, Charles J. Stone – Ebook PDF Instant Download/Delivery: 1478616997, 978-1478616993
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Product details:

ISBN 10: 1478616997
ISBN 13: 978-1478616993
Author: Paul Gerhard Hoel, Sidney C. Port, Charles J. Stone
Introduction to Stochastic Processes 1st Edition: An excellent introduction for electrical, electronics engineers and computer scientists who would like to have a good, basic understanding of the stochastic processes! This clearly written book responds to the increasing interest in the study of systems that vary in time in a random manner. It presents an introductory account of some of the important topics in the theory of the mathematical models of such systems. The selected topics are conceptually interesting and have fruitful application in various branches of science and technology.

 

Introduction to Stochastic Processes 1st Edition Table of contents:

Chapter 1: Markov Chains
1.1 Markov Chains Having Two States
1.2 Transition Function and Initial Distribution
1.3 Examples
1.4 Computations with Transition Functions

• 1.4.1 Hitting Times
• 1.4.2 Transition Matrix
  1.5 Transient and Recurrent States
  1.6 Decomposition of the State Space
• 1.6.1 Absorption Probabilities
• 1.6.2 Martingales
  1.7 Birth and Death Chains
  1.8 Branching and Queuing Chains
• 1.8.1 Branching Chain
• 1.8.2 Queuing Chain
  1.9 Proof of Results for the Branching and Queuing Chains
• 1.9.1 Branching Chain
• 1.9.2 Queuing Chain
  Exercises

Chapter 2: Stationary Distributions of a Markov Chain
2.1 Elementary Properties of Stationary Distributions
2.2 Examples

• 2.2.1 Birth and Death Chain
• 2.2.2 Particles in a Box
  2.3 Average Number of Visits to a Recurrent State
  2.4 Null Recurrent and Positive Recurrent States
  2.5 Existence and Uniqueness of Stationary Distributions
• 2.5.1 Reducible Chains
  2.6 Queuing Chain
• 2.6.1 Proof
  2.7 Convergence to the Stationary Distribution
  2.8 Proof of Convergence
• 2.8.1 Periodic Case
• 2.8.2 A Result from Number Theory
  Exercises

Chapter 3: Markov Pure Jump Processes
3.1 Construction of Jump Processes
3.2 Birth and Death Processes

• 3.2.1 Two-State Birth and Death Process
• 3.2.2 Poisson Process
• 3.2.3 Pure Birth Process
• 3.2.4 Infinite Server Queue
  3.3 Properties of a Markov Pure Jump Process
• 3.3.1 Applications to Birth and Death Processes
  Exercises

Chapter 4: Second Order Processes
4.1 Mean and Covariance Functions
4.2 Gaussian Processes
4.3 The Wiener Process
Exercises

Chapter 5: Continuity, Integration, and Differentiation of Second Order Processes
5.1 Continuity Assumptions

• 5.1.1 Continuity of the Mean and Covariance Functions
• 5.1.2 Continuity of the Sample Functions
  5.2 Integration
  5.3 Differentiation
  5.4 White Noise
  Exercises

Chapter 6: Stochastic Differential Equations, Estimation Theory, and Spectral Distributions
6.1 First-Order Differential Equations
6.2 Differential Equations of Order n

• 6.2.1 The Case n = 2
  6.3 Estimation Theory
• 6.3.1 General Principles of Estimation
• 6.3.2 Some Examples of Optimal Prediction
  6.4 Spectral Distribution

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