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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)

Lecture 31 - Conditional Arrival Times


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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