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Advanced Topics in Probability and Random Processes

Advanced Topics in Probability and Random Processes. Instructor: Prof. P. K. Bora, Department of Electronics and Electrical Engineering, IIT Guwahati. 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. (from nptel.ac.in)

Lecture 04 - Random Vectors and Random Processes

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Introduction to Probability and Random Variable

Lecture 01 - Probability Basics

Lecture 02 - Random Variable

Lecture 03 - Random Variable (cont.)

Random Process Basics and Infinite Sequence of Events

Lecture 04 - Random Vectors and Random Processes

Lecture 05 - Infinite Sequence of Events

Lecture 06 - Infinite Sequence of Events (cont.)

Convergence of a Sequence of Random Variables

Lecture 07 - Convergence of a Sequence of Random Variables

Lecture 08 - Weak Convergence

Lecture 09 - Weak Convergence (cont.)

Applications of Convergence Theory

Lecture 10 - Laws of Large Numbers

Lecture 11 - Central Limit Theorem

Lecture 12 - Large Deviation Theory

Markov Chain

Lecture 13 - Cramer's Theorem for Large Deviation

Lecture 14 - Introduction to Markov Processes

Discrete Time Markov Chain

Lecture 15 - Discrete Time Markov Chain 1

Lecture 16 - Discrete Time Markov Chain 2

Lecture 17 - Discrete Time Markov Chain 3

Lecture 18 - Discrete Time Markov Chain 4

Lecture 19 - Discrete Time Markov Chain 5

Continuous Time Markov Chain

Lecture 20 - Continuous Time Markov Chain 1

Lecture 21 - Continuous Time Markov Chain 2

Lecture 22 - Continuous Time Markov Chain 3

Martingale Process

Lecture 23 - Martingale Process

Lecture 24 - Martingale Process (cont.)