NOC:Introduction to Stochastic Processes


Lecture 1 - Sample Space and events


Lecture 2 - Axioms of Probability


Lecture 3 - Independence of events and Conditional Probability


Lecture 4 - Baye’s Theorem and Introduction to Random Variables


Lecture 5 - CDF and it’s properties


Lecture 6 - Continuity of Probability


Lecture 7 - Discrete and Continuous random variables


Lecture 8 - Expectation of random variables and its properties


Lecture 9 - Variance and some inequalities of random variables


Lecture 10 - Discrete Probability Distributions


Lecture 11 - Continuous Probability Distributions


Lecture 12 - Jointly distributed random variables and conditional distributions


Lecture 13 - Correlation and Covariance


Lecture 14 - Transformation of random vectors


Lecture 15 - Gaussian random vector and joint Gaussian distribution


Lecture 16 - Random Processes


Lecture 17 - Properties of random Process


Lecture 18 - Poisson Process


Lecture 19 - Properties of Poisson Process - Part 1


Lecture 20 - Properties of Poisson Process - Part 2


Lecture 21 - Convergence of sequence of random variables - Part 1


Lecture 22 - Convergence of sequence of random variables - Part 2


Lecture 23 - Relation between different notions of convergence


Lecture 24 - Cauchy’s criteria of convergence


Lecture 25 - Convergence in expectation


Lecture 26 - Law of Large Numbers


Lecture 27 - Central limit theorem


Lecture 28 - Chernoff bound


Lecture 29 - Introduction to Markov property


Lecture 30 - Transition Probability Matrix


Lecture 31 - Finite dimensional distribution of Markov chains


Lecture 32 - Strong Markov Property


Lecture 33 - Stopping Time


Lecture 34 - Hitting Times and Recurrence


Lecture 35 - Mean Number of returns to a state


Lecture 36 - Communicating classes and class properties


Lecture 37 - Class Properties (Continued...)


Lecture 38 - Positive Recurrence and The Invariant Probability Vector


Lecture 39 - Properties of Invariant Probability Vector


Lecture 40 - Condition For Transience


Lecture 41 - Example of Queue


Lecture 42 - Queue Continued and Example of Page Rank


Lecture 43 - Introduction to renewal Theory


Lecture 44 - The Elementary Renewal Theorem


Lecture 45 - Application to DTMC


Lecture 46 - Renewal Reward Theorem


Lecture 47 - Introduction to Continuous Time Markov Chains


Lecture 48 - Properties of states in CTMC


Lecture 49 - Embedded markov chain