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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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English
English [CC]
FREE
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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.
Course content
- Introduction and Probability Review Unlimited
- More Review; The Bernoulli Process Unlimited
- Law of Large Numbers, Convergence Unlimited
- Poisson (The Perfect Arrival Process) Unlimited
- Poisson Combining and Splitting Unlimited
- From Poisson to Markov Unlimited
- Finite State Markov Chains; The Matrix Approach Unlimited
- Markov Eigenvalues and Eigenvectors Unlimited
- Markov Rewards and Dynamic Programming Unlimited
- Renewals and The Strong Law of Large Numbers Unlimited
- Renewals; Strong Law and Rewards Unlimited
- Renewal Rewards Stopping Trials and Walds Inequality Unlimited
- Little, M/G/1, Ensemble Averages Unlimited
- Review Unlimited
- The Last Renewal Unlimited
- Renewals and Counta-State Markovble Unlimited
- Countable-State Markov Chains Unlimited
- Countable-State Markov Chains and Processes Unlimited
- Countable-State Markov Processes Unlimited
- Markov Processes and Random Walks Unlimited
- Hypothesis Testing and Random Walks Unlimited
- Random Walks and Thresholds Unlimited
- Martingales (Plain, Sub, and Super) Unlimited
- Martingales: Stopping and Converging Unlimited
- Putting it all Together Unlimited
Instructor
Massachusetts Institute of Technology
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