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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.

Course Information

Source	MIT 開放式課程
科系	Electrical Engineering and Computer Science
Language	English
影片數	25

課程影片 (25)

1. Introduction and Probability Review

1. Introduction and Probability Review

2. More Review; The Bernoulli Process

2. More Review; The Bernoulli Process

3. Law of Large Numbers, Convergence

3. Law of Large Numbers, Convergence

4. Poisson (the Perfect Arrival Process)

4. Poisson (the Perfect Arrival Process)

5. Poisson Combining and Splitting

5. Poisson Combining and Splitting

6. From Poisson to Markov

6. From Poisson to Markov

7. Finite-state Markov Chains; The Matrix Approach

7. Finite-state Markov Chains; The Matrix Approach

8. Markov Eigenvalues and Eigenvectors

8. Markov Eigenvalues and Eigenvectors

9. Markov Rewards and Dynamic Programming

9. Markov Rewards and Dynamic Programming

10. Renewals and the Strong Law of Large Numbers

10. Renewals and the Strong Law of Large Numbers

11. Renewals: Strong Law and Rewards

11. Renewals: Strong Law and Rewards

12. Renewal Rewards, Stopping Trials, and Wald's Inequality

12. Renewal Rewards, Stopping Trials, and Wald's Inequality

13. Little, M/G/1, Ensemble Averages

13. Little, M/G/1, Ensemble Averages

15. The Last Renewal

15. The Last Renewal

16. Renewals and Countable-state Markov

16. Renewals and Countable-state Markov

17. Countable-state Markov Chains

17. Countable-state Markov Chains

18. Countable-state Markov Chains and Processes

18. Countable-state Markov Chains and Processes

19. Countable-state Markov Processes

19. Countable-state Markov Processes

20. Markov Processes and Random Walks

20. Markov Processes and Random Walks

21. Hypothesis Testing and Random Walks

21. Hypothesis Testing and Random Walks

22. Random Walks and Thresholds

22. Random Walks and Thresholds

23. Martingales (Plain, Sub, and Super)

23. Martingales (Plain, Sub, and Super)

24. Martingales: Stopping and Converging

24. Martingales: Stopping and Converging

25. Putting It All Together

25. Putting It All Together