Discrete Stochastic Processes
Massachusetts Institute of Technology via MIT OpenCourseWare
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Overview
Syllabus
1. Introduction and Probability Review.
2. More Review; The Bernoulli Process.
3. Law of Large Numbers, Convergence.
4. Poisson (the Perfect Arrival Process).
5. Poisson Combining and Splitting.
6. From Poisson to Markov.
7. Finite-state Markov Chains; The Matrix Approach.
8. Markov Eigenvalues and Eigenvectors.
9. Markov Rewards and Dynamic Programming.
10. Renewals and the Strong Law of Large Numbers.
11. Renewals: Strong Law and Rewards.
12. Renewal Rewards, Stopping Trials, and Wald's Inequality.
13. Little, M/G/1, Ensemble Averages.
14. Review.
15. The Last Renewal.
16. Renewals and Countable-state Markov.
17. Countable-state Markov Chains.
18. Countable-state Markov Chains and Processes.
19. Countable-state Markov Processes.
20. Markov Processes and Random Walks.
21. Hypothesis Testing and Random Walks.
22. Random Walks and Thresholds.
23. Martingales (Plain, Sub, and Super).
24. Martingales: Stopping and Converging.
25. Putting It All Together.
Taught by
Prof. Robert Gallager