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Diagram of two stable M/M/1 queues.

Course6.26225 lectures33 h 4 min

Discrete Stochastic Processes

Prof. Robert Gallager · Massachusetts Institute of Technology

Start with lecture 1 At MIT OpenCourseWare

About

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.

Lectures

Video Lectures

  1. Lecture 1: Introduction and Probability Review 1 h 17 min · Video
  2. Lecture 2: More Review; The Bernoulli Process 1 h 9 min · Video
  3. Lecture 3: Law of Large Numbers, Convergence 1 h 22 min · Video
  4. Lecture 4: Poisson (The Perfect Arrival Process) 1 h 18 min · Video
  5. Lecture 5: Poisson Combining and Splitting 1 h 25 min · Video
  6. Lecture 6: From Poisson to Markov 1 h 20 min · Video
  7. Lecture 7: Finite-state Markov Chains; The Matrix Approach 56 min · Video
  8. Lecture 8: Markov Eigenvalues and Eigenvectors 1 h 24 min · Video
  9. Lecture 9: Markov Rewards and Dynamic Programming 1 h 24 min · Video
  10. Lecture 10: Renewals and the Strong Law of Large Numbers 1 h 22 min · Video
  11. Lecture 11: Renewals: Strong Law and Rewards 1 h 19 min · Video
  12. Lecture 12: Renewal Rewards, Stopping Trials, and Wald's Inequality 1 h 27 min · Video
  13. Lecture 13: Little, M/G/1, Ensemble Averages 1 h 15 min · Video
  14. Lecture 14: Review 1 h 20 min · Video
  15. Lecture 15: The Last Renewal 1 h 16 min · Video
  16. Lecture 16: Renewals and Countable-state Markov 1 h 20 min · Video
  17. Lecture 17: Countable-state Markov Chains 1 h 24 min · Video
  18. Lecture 18: Countable-state Markov Chains and Processes 1 h 17 min · Video
  19. Lecture 19: Countable-state Markov Processes 1 h 23 min · Video
  20. Lecture 20: Markov Processes and Random Walks 1 h 24 min · Video
  21. Lecture 21: Hypothesis Testing and Random Walks 1 h 26 min · Video
  22. Lecture 22: Random Walks and Thresholds 1 h 22 min · Video
  23. Lecture 23: Martingales (Plain, Sub, and Super) 1 h 23 min · Video
  24. Lecture 24: Martingales: Stopping and Converging 1 h 21 min · Video
  25. Lecture 25: Putting It All Together 1 h 22 min · Video

Syllabus and materials

At MIT OpenCourseWare, as the course publishes them.

Credits and licence

Institution
Massachusetts Institute of Technology
Department
Electrical Engineering and Computer Science
Teacher
Prof. Robert Gallager
Term
Spring 2011
Level
Graduate
Language
English
Subjects
Mathematics, Computer science, Engineering
Source
MIT OpenCourseWare
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
Attribution
Prof. Robert Gallager. Discrete Stochastic Processes. Spring 2011. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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