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Course11010114150 lectures

Introduction to Stochastic Processes

Prof. Manjesh Hanawal · IIT Bombay

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Lecture 1: Sample Space and events Video
  2. Lecture 2: Axioms of Probability Video
  3. Lecture 3: Independence of events and Conditional Probability Video
  4. Lecture 4: Baye's Theorem and Introduction to Random Variables Video

Week 2

  1. Lecture 5: CDF and it's properties Video
  2. Lecture 6: Continuity of Probability Video
  3. Lecture 7: Discrete and Continuous random variables Video
  4. Lecture 8: Expectation of random variables and its properties Video

Week 3

  1. Lecture 9: Variance and some inequalities of random variables Video
  2. Lecture 10: Discrete Probability Distributions Video
  3. Lecture 11: Continuous Probability Distributions Video
  4. Lecture 12: Jointly distributed random variables and conditional distributions Video

Week 4

  1. Lecture 13: Correlation and Covariance Video
  2. Lecture 14: Transformation of random vectors Video
  3. Lecture 15: Gaussian random vector and joint Gaussian distribution Video

Week 5

  1. Lecture 16: Random Processes Video
  2. Lecture 17: Properties of random Process Video
  3. Lecture 18: Poisson Process Video
  4. Lecture 19: Properties of Poisson Process (Part 1) Video
  5. Lecture 20: Properties of Poisson Process (Part 2) Video

Week 6

  1. Lecture 21: Convergence of sequence of random variables (Part 1) Video
  2. Lecture 22: Convergence of sequence of random variables (Part 2) Video
  3. Lecture 23: Relation between different notions of convergence Video
  4. Lecture 24: Cauchy's criteria of convergence Video

Week 7

  1. Lecture 25: Convergence in expectation Video
  2. Lecture 26: Law of Large Numbers Video
  3. Lecture 27: Central limit theorem Video
  4. Lecture 28: chernoff bound Video

Week 8

  1. Lecture 29: Introduction to Markov property Video
  2. Lecture 30: Transition Probability Matrix Video
  3. Lecture 31: Finite dimensional distribution of Markov chains Video

Week 9

  1. Lecture 32: Strong Markov Property Video
  2. Lecture 33: Stopping Time Video
  3. Lecture 34: Hitting Times and Recurrence Video
  4. Lecture 35: Mean Number of returns to a state Video

Week 10

  1. Lecture 36: Communicating classes and class properties Video
  2. Lecture 37: Class Properties Continued Video
  3. Lecture 38: Positive Recurrence and The Invariant Probability Vector Video
  4. Lecture 39: Properties of Invariant Probability Vector Video

Week 11

  1. Lecture 40: Condition For Transience Video
  2. Lecture 41: Example of Queue Video
  3. Lecture 42: Queue Continued and Example of Page Rank Video
  4. Lecture 43: Introduction to renewal Theory Video

Extra Content

  1. Lecture 44: The Elementary Renewal Theorem Video
  2. Lecture 45: Application to DTMC Video
  3. Lecture 46: Renewal Reward Theorem Video

Week 13

  1. Lecture 47: Introduction to Continuous Time Markov Chains Video
  2. Lecture 48: Properties of states in CTMC Video
  3. Lecture 49: Embedded markov chain Video

Live Session

  1. Live Session 18-02-2020 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Management
Teacher
Prof. Manjesh Hanawal
Level
Undergraduate
Language
English
Subjects
Business and management
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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