# InfoCoBuild

## 6.262 Discrete Stochastic Processes

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. 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)

 Introduction

 Lecture 01 - Introduction and Probability Review Lecture 02 - More Review; The Bernoulli Process Lecture 03 - Law of Large Numbers, Convergence Lecture 04 - Poisson (the Perfect Arrival Process) Lecture 05 - Poisson Combining and Splitting Lecture 06 - From Poisson to Markov Lecture 07 - Finite-state Markov Chains; The Matrix Approach Lecture 08 - Markov Eigenvalues and Eigenvectors Lecture 09 - Markov Rewards and Dynamic Programming Lecture 10 - Renewals and the Strong Law of Large Numbers Lecture 11 - Renewals: Strong Law and Rewards Lecture 12 - Renewal Rewards, Stopping Trials, and Wald's Inequality Lecture 13 - Little, M/G/1, Ensemble Averages Lecture 14 - Review Lecture 15 - The Last Renewal Lecture 16 - Renewals and Countable-state Markov Lecture 17 - Countable-state Markov Chains Lecture 18 - Countable-state Markov Chains and Processes Lecture 19 - Countable-state Markov Processes Lecture 20 - Markov Processes and Random Walks Lecture 21 - Hypothesis Testing and Random Walks Lecture 22 - Random Walks and Thresholds Lecture 23 - Martingales (Plain, Sub, and Super) Lecture 24 - Martingales: Stopping and Converging Lecture 25 - Putting It All Together

 References 6.262 - Discrete Stochastic Processes (Spring 2011) Instructor: Professor Robert Gallager. Course Notes. Lecture Slides. Assignments and Solutions. Exams and Solutions. Download Course Materials.