Discrete-Time Markov Chains and Poisson Processes (Prof. Ayon Ganguly, IIT Guwahati) | Mathematics

Discrete-Time Markov Chains and Poisson Processes

Discrete-Time Markov Chains and Poisson Processes. Instructor: Prof. Ayon Ganguly, Department of Mathematics, IIT Guwahati. In this course we will cover discrete-time Markov chains and Poisson Processes. Knowledge of basic probability is essential for this course. The mathematical rigor of the course will be at an undergraduate level. We will cover from basic definition to limiting probabilities for both discrete -time Markov chains. We will discuss in detail Poisson processes, the simplest example of a continuous-time Markov chain. The course will involve a lot of illustrative examples and worked out problems. (from nptel.ac.in)

Introduction

Lecture 01 - Review of Basic Probability I

Lecture 02 - Review of Basic Probability II

Lecture 03 - Review of Basic Probability III

Lecture 04 - Stochastic Processes

Lecture 05 - Definition of Markov Chain and Transition Probabilities

Lecture 06 - Markov Property and Chapman-Kolmogorov Equations

Lecture 07 - Chapman-Kolmogorov Equations: Examples

Lecture 08 - Accessibility and Communication of States

Lecture 09 - Hitting Time I

Lecture 10 - Hitting Time II

Lecture 11 - Hitting Time III

Lecture 12 - Strong Markov Property

Lecture 13 - Passage Time and Excursion

Lecture 14 - Number of Visits

Lecture 15 - Class Property

Lecture 16 - Transience and Recurrence of Random Walks

Lecture 17 - Stationary Distribution I

Lecture 18 - Stationary Distribution II

Lecture 19 - Stationary Distribution III

Lecture 20 - Limit Theorems I

Lecture 21 - Limit Theorems II

Lecture 22 - Some Problems I

Lecture 23 - Some Problems II

Lecture 24 - Time Reversibility

Lecture 25 - Properties of Exponential Distribution

Lecture 26 - Some Problems

Lecture 27 - Order Statistics

Lecture 28 - Poisson Processes

Lecture 29 - Poisson Thinning I

Lecture 30 - Poisson Thinning II

Lecture 31 - Conditional Arrival Times

Lecture 32 - Independent Poisson Processes

Lecture 33 - Some Problems

Lecture 34 - Compound Poisson Processes

References

Discrete-Time Markov Chains and Poisson Processes
Instructor: Prof. Ayon Ganguly, Department of Mathematics, IIT Guwahati. In this course we will cover discrete-time Markov chains and Poisson Processes.