Advanced Topics in Probability and Random Processes

Course Intro: The course will cover mainly two broad areas: (1) the concepts of the convergence a sequence of random variables leading to the explanation of important concepts like the laws of large numbers, central limit theorem; and (2) Markov chains that include the analysis of discrete and continuous time Markov Chains and their applications.

Pre Requisites: Basic Course in Probability

Advanced Topics in Probability and Random Processes.
Lec 1: Probability Basics.
Lec 2: Random Variable-I.
Lec 3: Random Variable-II.
Lec 4: Random Vectors and Random Processes.
Lec 5: Infinite Sequence of Events-l.
Lec 6: Infinite Sequence of Events-ll.
Lec 7: Convergence of Sequence of Random Variables.
Lec 8: Weak Convergence-I.
Lec 9: Weak Convergence-II.
Lec 10: Laws of Large Numbers.
Lec 11: Central Limit Theorem.
Lec 12: Large Deviation Theory.
Lec 13: Crammer's Theorem for Large Deviation.
Lec 14: Introduction to Markov Processes.
Lec 15: Discrete Time Markov Chain.
Lec 16: Discrete Time Markov Chain-2.
Lec 17: Discrete Time Markov Chain-3.
Lec 18: Discrete Time Markov Chain-4.
Lec 19: Discrete Time Markov Chain-5.
Lec 20: Continuous Time Markov Chain - 1.
Lec 21: Continuous Time Markov Chain - 2.
Lec 22: Continuous Time Markov Chain - 3.
Lec 23: Martingle Process-1.
Lec 24: Martingle Process-2.