18.175
Theory of Probability
Spring 2014
Topics
- Probability Spaces and Sigma-Algebras
- Extension Theorems: A Tool for Constructing Measures
- Random Variables and Distributions
- Integration
- More Integration and Expectation
- Laws of Large Numbers and Independence
- Sums of Random Variables
- Weak Laws and Moment-Generating and Characteristic Functions
- Borel-Cantelli and the Strong Law of Large Numbers
- Zero-One Laws and Maximal Inequalities
- Independent Sums and Large Deviations
- DeMoivre-Laplace and Weak Convergence
- Large Deviations
- Weak Convergence and Characteristic Functions
- Characteristic Functions and Central Limit Theorem
- Central Limit Theorem Variants
- Poisson Random Variables
- Stable Random Variables
- Higher Dimensional Limit Theorems
- Infinite Divisibility and Levy Processes
- More on Infinite Divisibility and Levy Processes
- Random Walks
- More on Random Walks
- Reflections and Martingales
- More on Martingales
- More on Martingales (cont.)
- Even More on Martingales
- Still More Martingales
- Markov Chains
- More Markov Chains
- Additional Material on Markov Chains
- Ergodic Theory
- More Ergodic Theory
- Brownian Motion
- More Brownian Motion
- Even More Brownian Motion
- Last Lecture
Readings
- This course will follow the textbook:
- In addition to the main textbook, there are many excellent textbooks and sets of lecture notes that cover the material of this course, several written by people right here at MIT. The course material is contained in the union of the following online texts for first-year graduate probability courses:
- Williams, David. Probability with Martingales . China Press, 2008. ISBN: 9787506292511.
Sources
- Course catalogue ↗Historical OpenCourseWare
- MIT OCW readings ↗
- MIT OCW calendar ↗
- MIT OCW syllabus ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.