Catalog

Discrete Stochastic Processes

Electrical Engineering and Computer Science MIT CC BY-NC-SA 4.0 25 lectures

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.

Syllabus

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

Course materials