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This course is an introduction to Markov chains, random walks, martingales, and Galton-Watsom tree.
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English
English [CC]
FREE
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Description
The course requires basic knowledge in probability theory and linear algebra including conditional expectation and matrix.
Course content
- Introduction to Finite Markov Chains Unlimited
- Markov Chains: Stationary Distribution Unlimited
- Markov Chains: Time-reversal Unlimited
- Introduction to Markov Chain Mixing Unlimited
- Stationary Times Unlimited
- Lower Bounds on Mixing Times Unlimited
- Summary on Mixing Times Unlimited
- Random Walk on Networks 1 Unlimited
- Random Walk on Networks 2 Unlimited
- Hitting Times Unlimited
- Summary on Random Walk on Networks Unlimited
- Countable State Space Chain 1 Unlimited
- Countable State Space Chain 2 Unlimited
- Conditional Expectation and Introduction to Martingales Unlimited
- Martingales: Optional Stopping Theorem Unlimited
- Martingales: Convergence Unlimited
- Almost Sure Convergence Unlimited
- Martingales: Uniformly Integrable Unlimited
- Galton-Watson Tree Unlimited
- Poisson Process Unlimited
- Continuous Time Markov Chain Unlimited
- Infinitesimal Generator Unlimited
- Irreducible and Recurrence Unlimited
- Stationary Distribution Unlimited
Instructor
Massachusetts Institute of Technology
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1916
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