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Created by:
Last updated:
November 3, 2022
Duration:
Unlimited Duration
FREE
This course includes:
Unlimited Duration
Badge on Completion
Certificate of completion
Unlimited Duration
Description
This class covers the analysis and modeling of stochastic processes.
Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models
Course Curriculum
- Metric spaces Unlimited
- Large deviations technique Unlimited
- Cramér’s theorem Unlimited
- Applications of large deviations Unlimited
- LD in many dimensions and Markov chains Unlimited
- Intro Brownian motion Unlimited
- Brownian motion Unlimited
- Quadratic variation Unlimited
- Filtration and martingales Unlimited
- Martingales I Unlimited
- Martingales II Unlimited
- Additional materials: Martingale convergence theorem Unlimited
- Martigales concentration inequality Unlimited
- Talagrand’s concentration inequality Unlimited
- Ito calculus Unlimited
- Ito construction Unlimited
- Ito integral Unlimited
- Ito process and formula Unlimited
- Ito applications Unlimited
- Weak convergence Unlimited
- Tightness of measures Unlimited
- Reflected Brownian motion Unlimited
About the instructor
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Massachusetts Institute of Technology
