Discrete ,Stochastic, Processes, free videos and free material uploaded by Massachusetts Institute of Technology Staff .
1Introduction and probability review
2More review; the Bernoulli process
3Laws of large numbers, convergence
4Poisson (the perfect arrival process)
5Poisson combining and splitting
6From Poisson to Markov
7Finite-state Markov chains; the matrix
approach
8Markov eigenvalues and eigenvectors
9Markov rewards and dynamic programming
10Renewals and the strong law of large numbers
(SLLN)
11Renewals: strong law and rewards
12Renewal rewards, stopping trials, and Wald's
equality
13Little, M/G/1, ensemble averages
14Review
15The last
16Renewals and countable state Markov
17Countable-state Markov chains
18Countable-state Markov chains and
19Countable-state Markov
20Markov processes and random walks
21Hypothesis testing and random
22Random walks and thresholds
23Martingales (plain, sub and super)
24Martingales: stopping and converging
25Putting it all together
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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