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Discrete Stochastic Processes

Stochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understand...

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Bibliographic Details
Main Author: Gallager, Robert G.
Format: eBook
Language:English
Published: New York, NY Springer US 1996, 1996
Edition:1st ed. 1996
Series:The Springer International Series in Engineering and Computer Science
Subjects:
Operations Research
Electrical And Electronic Engineering
Electrical Engineering
Operations Research And Decision Theory
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 7.2 The G/G/1 Queue
  • 7.3 Detection, Decisions, and Hypothesis Testing
  • 7.4 Threshold Crossing Probabilities
  • 7.5 Wald’s Identity and Walks with Two Thresholds
  • 7.6 Martingales and Submartingales
  • 7.7 Stopped Processes and Stopping Rules
  • 7.8 The Kolmogorov Inequalities
  • 7.9 Summary
  • Exercises
  • Notes
  • 4 Finite State Markov Chains
  • 4.1 Introduction
  • 4.2 Classification of States
  • 4.3 The Matrix Representation
  • 4.4 Perron—Frobenius Theory
  • 4.5 Markov Chains with Rewards
  • 4.6 Markov Decision Theory and Dynamic Programming
  • 4.7 Summary
  • Exercises
  • Notes
  • 5 Markov Chains with Countably Infinite State Spaces
  • 5.1 Introduction and Classification of States
  • 5.2 Branching Processes
  • 5.3 Birth Death Markov Chains
  • 5.4 Reversible Markov Chains
  • 5.5 The M/M/1 Sampled Time Markov Chain
  • 5.6 Round-Robin and Processor Sharing
  • 5.7 Semi-Markov Processes
  • 5.8 Example—M/G/1 Queue
  • 5.9 Summary
  • Exercises
  • 6 Markov Processes with Countable State Spaces
  • 6.1 Introduction
  • 6.2 The Kolmogorov Differential Equations
  • 6.3 Uniformization
  • 6.4 Birth Death Processes
  • 6.5 Reversibility for Markov Processes
  • 6.6 Jackson Networks
  • ClosedJackson Networks
  • 6.7 Summary
  • Exercises
  • 7 Random Walks and Martingales
  • 7.1 Introduction
  • 1 Introduction and Probability Review
  • 1.1 Introduction
  • 1.2 Probability Review
  • 1.3 Conditional Probabilities
  • 1.4 Random Variables
  • 1.5 Expectations
  • 1.6 Transforms
  • 1.7 Weak Law of Large Numbers
  • 1.8 Strong Law of Large Numbers
  • 1.9 Summary
  • Table of Standard Random Variables
  • Exercises
  • Notes
  • 2 Poisson Processes
  • 2.1 Introduction
  • 2.2 Definition and Properties of the Poisson Process
  • 2.3 Combinations and Subdivisions of Independent Poisson Processes
  • 2.4 Non-Homogeneous Poisson Processes
  • 2.5 Order Statistics and Conditional Arrival Epochs
  • 2.6 Summary
  • Exercises
  • Notes
  • 3 Renewal Processes
  • 3.1 Introduction
  • 3.2 Strong Law of Large Numbers for Renewal Processes
  • 3.3 Expected Number of Renewals
  • 3.4 Renewal Reward Processes; Time Averages
  • 3.5 Renewal Reward Processes; Ensemble Averages
  • 3.6 Applications of Renewal Reward Theory
  • 3.7 Delayed Renewal Processes
  • 3.8 Summary
  • Exercises
  • Notes

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