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Course11110315835 lectures

Discrete-time Markov Chains And Poisson Processes

Prof. Ayon Ganguly and Prof. Subhamay Saha · IIT Guwahati

Start with lecture 1 At NPTEL

Lectures

Week 1: Introduction to Discrete-time Markov Chains

  1. Lec 1: Review of Basic Probability I Video
  2. Lec 2: Review of Basic Probability II Video
  3. Lec 3: Review of Basic Probability III Video
  4. Lec 4: Stochastic Processes Video
  5. Lec 5: Definition of Markov Chain and Transition Probabilities Video

Week 2: Chapman-Kolmogorov Equations and Communication

  1. Lec 6: Markov Property and Chapman-Kolmogorov Equations Video
  2. Lec 7: Chapman-Kolmogorov Equations: Examples Video
  3. Lec 8: Accessibility and Communication of States Video

Week 3: Hitting Times and Strong Markov Property

  1. Lec 9: Hitting Time I Video
  2. Lec 10: Hitting Time II Video
  3. Lec 11: Hitting Time III Video
  4. Lec 12: Strong Markov Property Video

Week 4: Classification of States

  1. Lec 13: Passage Time and Excursion Video
  2. Lec 14: Number of Visits Video
  3. Lec 15: Class Property Video
  4. Lec 16: Transience and Recurrence of Random Walks Video

Week 5: Stationary Distribution

  1. Lec 17: Stationary Distribution I Video
  2. Lec 18: Stationary Distribution II Video
  3. Lec 19: Stationary Distribution III Video

Week 6: Limit Theorems & Time Reversibility

  1. Lec 20: Limit Theorems I Video
  2. Lec 21: Limit Theorems II Video
  3. Lec 22: Some Problems I Video
  4. Lec 23: Some Problems II Video
  5. Lec 24: Time Reversibility Video

Week 7: Exponential Distribution and Poisson Processes

  1. Lec 25: Properties of Exponential Distribution Video
  2. Lec 26: Some Problems Video
  3. Lec 27: Order Statistics Video
  4. Lec 28: Poisson Processes Video

Week 8: Poisson Processes

  1. Lec 29: Poisson Thinning I Video
  2. Lec 30: Poisson Thinning II Video
  3. Lec 31: Conditional Arrival Times Video
  4. Lec 32: Independent Poisson Processes Video
  5. Lec 33: Some Problems Video
  6. Lec 34: Compound Poisson Processes Video

Live Session

  1. Live Session 15-03-2022 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Guwahati
Department
Mathematics
Taught by
Prof. Ayon Ganguly, Prof. Subhamay Saha
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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