Nguồn ngoài
Discrete Stochastic Processes
Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This text aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding.
- Tác giả
- Robert Gallager
- Nhà xuất bản
- Massachusetts Institute of Technolog
- Nguồn
- LibreTexts
- Giấy phép
- CC BY-NC-SA
- Ngôn ngữ
- EN
Mục lục· 70 mục
- 01: Introduction and Review of Probability
- 1.01: Probability Models
- 1.02: The Axioms of Probability Theory
- 1.03: Probability Review
- 1.04: Basic Inequalities
- 1.05: The Laws of Large Numbers
- 1.06: Relation of Probability Models to the Real World
- 1.07: Summary
- 1.08: Exercises
- 02: Poisson Processes
- 2.01: Introduction to Poisson Processes
- 2.02: Definition and Properties of a Poisson Process
- 2.03: Combining and Splitting Poisson Processes
- 2.04: Non-homogeneous Poisson Processes
- 2.05: Conditional Arrival Densities and Order Statistics
- 2.06: Summary
- 2.07: Exercises
- 03: Finite-State Markov Chains
- 3.01: Introduction to Finite-state Markov Chains
- 3.02: Classification of States
- 3.03: The Matrix Representation
- 3.04: The Eigenvalues and Eigenvectors of Stochastic Matrices
- 3.05: Markov Chains with Rewards
- 3.06: Markov Decision Theory and Dynamic Programming
- 3.07: Summary
- 3.08: Exercises
- 04: Renewal Processes
- 4.01: Introduction
- 4.02: The Strong Law of Large Numbers and Convergence WP1
- 4.03: Strong Law for Renewal Processes
- 4.04: Renewal-Reward Processes and Time-Averages
- 4.05: Random Stopping Trials
- 4.06: Expected Number of Renewals
- 4.07: Renewal-reward processes ensemble-averages
- 4.8: Delayed Renewal Processes
- 4.9: Summary
- 4.10: Exercises
- 05: Countable-state Markov Chains
- 5.01: Countable State Markov Chains
- 5.02: Birth-Death Markov chains
- 5.03: Reversible Markov Chains
- 5.04: The M M 1 sample-time Markov chain
- 5.5: Branching Processes
- 5.6: Round-robin and Processor Sharing
- 5.7: Summary
- 5.8: Exercises
- 06: Markov processes with countable state spaces
- 6.01: Introduction
- 6.02: Steady State Behavior of Irreducible Markov Processes
- 6.03: The Kolmogorov Differential Equations
- 6.04: Uniformization
- 6.05: Birth-Death Processes
- 6.06: Reversibility for Markov Processes
- 6.7: Jackson Networks
- 6.8: Semi-Markov Processes
- 6.9: Summary
- 6.10: Excercises
- 07: Random Walks Large Deviations and Martingales
- 7.01: Introduction
- 7.02: The Queueing Delay in a G G 1 Queue
- 7.03: Detection Decisions and Hypothesis Testing
- 7.04: Threshold Crossing Probabilities in Random Walks
- 7.05: Thresholds Stopping Rules and Wald's Identity
- 7.06: Martingales
- 7.07: Submartingales and Supermartingales
- 7.08: Stopping Processes and Stopping Trials
- 7.09: The Kolmogorov Inequalities
- 7.10: Markov Modulated Random Walks
- 7.11: Summary
- 7.12: Exercises