6.262 Discrete Stochastic Processes
25 Lectures · Jan 15, 2011
About
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.
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Lecture 1: Introduction to Discrete Stochastic Processes and Probability Review
Feb 11, 2013
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7518 Views
Lecture 2: More Review; The Bernoulli Process
Feb 11, 2013
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Lecture 3: Law of Large Numbers, Convergence
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Lecture 4: Poisson (The Perfect Arrival Process)
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Lecture 5: Poisson Combining and Splitting
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Lecture 6: From Poisson to Markov
Feb 11, 2013
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Lecture 7: Finite-state Markov Chains; The Matrix Approach
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Lecture 8: Markov Eigenvalues and Eigenvectors
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Lecture 9: Markov Rewards and Dynamic Programming
Feb 11, 2013
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Lecture 10: Renewals and the Strong Law of Large Numbers
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Lecture 11: Renewals: Strong Law and Rewards
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Lecture 12: Renewal Rewards, Stopping Trials, and Wald's Inequality
Feb 11, 2013
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Lecture 18: Countable-state Markov Chains and Processes
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Lecture 13: Little, M/G/1, Ensemble Averages
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Lecture 14: Review
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Lecture 15: The Last Renewal
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Lecture 16: Renewals and Countable-state Markov
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Lecture 17: Countable-state Markov Chains
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Lecture 19: Countable-state Markov Processes
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Lecture 20: Markov Processes and Random Walks
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Lecture 21: Hypothesis Testing and Random Walks
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Lecture 22: Random Walks and Thresholds
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Lecture 23: Martingales (Plain, Sub, and Super)
Feb 11, 2013
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Lecture 24: Martingales: Stopping and Converging
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Lecture 25: Putting It All Together
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