6.262 Discrete Stochastic Processes (Spring 2011, MIT OCW). Instructor: Professor Robert Gallager. Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals.
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September 21, 2023
English
English [CC]
Description
This course aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding, and includes many applications in engineering, physics, biology, operations research and finance. (from ocw.mit.edu)
Course Curriculum
- Lecture 01 – Introduction and Probability Review Unlimited
- Lecture 02 – More Review; The Bernoulli Process Unlimited
- Lecture 03 – Law of Large Numbers, Convergence Unlimited
- Lecture 04 – Poisson (the Perfect Arrival Process) Unlimited
- Lecture 05 – Poisson Combining and Splitting Unlimited
- Lecture 06 – From Poisson to Markov Unlimited
- Lecture 07 – Finite-state Markov Chains; The Matrix Approach Unlimited
- Lecture 08 – Markov Eigenvalues and Eigenvectors Unlimited
- Lecture 09 – Markov Rewards and Dynamic Programming Unlimited
- Lecture 10 – Renewals and the Strong Law of Large Numbers Unlimited
- Lecture 11 – Renewals: Strong Law and Rewards Unlimited
- Lecture 12 – Renewal Rewards, Stopping Trials, and Wald’s Inequality Unlimited
- Lecture 13 – Little, M/G/1, Ensemble Averages Unlimited
- Lecture 14 – Review Unlimited
- Lecture 15 – The Last Renewal Unlimited
- Lecture 16 – Renewals and Countable-state Markov Unlimited
- Lecture 17 – Countable-state Markov Chains Unlimited
- Lecture 18 – Countable-state Markov Chains and Processes Unlimited
- Lecture 19 – Countable-state Markov Processes Unlimited
- Lecture 20 – Markov Processes and Random Walks Unlimited
- Lecture 21 – Hypothesis Testing and Random Walks Unlimited
- Lecture 22 – Random Walks and Thresholds Unlimited
- Lecture 23 – Martingales (Plain, Sub, and Super) Unlimited
- Lecture 24 – Martingales: Stopping and Converging Unlimited
- Lecture 25 – Putting It All Together Unlimited
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