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Uedu Open / Discrete Stochastic Processes
6.262

Discrete Stochastic Processes

Prof. Robert Gallager | Spring 2011
Science & Math Mathematics Discrete Mathematics Probability and Statistics
前往原始課程
CC BY-NC-SA 4.0
課程簡介
Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This course 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, and includes many applications in engineering, physics, biology, operations research and finance.
課程資訊
來源MIT 開放式課程
科系Electrical Engineering and Computer Science
語言English
影片數25
課程影片 (25)
1
1. Introduction and Probability Review
1. Introduction and Probability Review
2
2. More Review; The Bernoulli Process
2. More Review; The Bernoulli Process
3
3. Law of Large Numbers, Convergence
3. Law of Large Numbers, Convergence
4
4. Poisson (the Perfect Arrival Process)
4. Poisson (the Perfect Arrival Process)
5
5. Poisson Combining and Splitting
5. Poisson Combining and Splitting
6
6. From Poisson to Markov
6. From Poisson to Markov
7
7. Finite-state Markov Chains; The Matrix Approach
7. Finite-state Markov Chains; The Matrix Approach
8
8. Markov Eigenvalues and Eigenvectors
8. Markov Eigenvalues and Eigenvectors
9
9. Markov Rewards and Dynamic Programming
9. Markov Rewards and Dynamic Programming
10
10. Renewals and the Strong Law of Large Numbers
10. Renewals and the Strong Law of Large Numbers
11
11. Renewals: Strong Law and Rewards
11. Renewals: Strong Law and Rewards
12
12. Renewal Rewards, Stopping Trials, and Wald's Inequality
12. Renewal Rewards, Stopping Trials, and Wald's Inequality
13
13. Little, M/G/1, Ensemble Averages
13. Little, M/G/1, Ensemble Averages
14
14. Review
14. Review
15
15. The Last Renewal
15. The Last Renewal
16
16. Renewals and Countable-state Markov
16. Renewals and Countable-state Markov
17
17. Countable-state Markov Chains
17. Countable-state Markov Chains
18
18. Countable-state Markov Chains and Processes
18. Countable-state Markov Chains and Processes
19
19. Countable-state Markov Processes
19. Countable-state Markov Processes
20
20. Markov Processes and Random Walks
20. Markov Processes and Random Walks
21
21. Hypothesis Testing and Random Walks
21. Hypothesis Testing and Random Walks
22
22. Random Walks and Thresholds
22. Random Walks and Thresholds
23
23. Martingales (Plain, Sub, and Super)
23. Martingales (Plain, Sub, and Super)
24
24. Martingales: Stopping and Converging
24. Martingales: Stopping and Converging
25
25. Putting It All Together
25. Putting It All Together