This course covers the analysis and modeling of stochastic processes. The aim of this course is to cover 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 course will go over some important applications to finance theory, insurance, queuing and inventory models.
Assessment
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
Certification
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Course Credit: MIT
Course Curriculum
| Module 01 | |||
| Metric spaces and topology | 00:15:00 | ||
| Large deviations technique | 00:15:00 | ||
| Cramér’s theorem | 00:15:00 | ||
| Applications of large deviations | 00:20:00 | ||
| LD in many dimensions and Markov | 00:00:00 | ||
| Intro Brownian motion | 00:15:00 | ||
| Brownian motion | 00:20:00 | ||
| Quadratic variation | 00:20:00 | ||
| Filtration and martingales | 00:10:00 | ||
| Martingales I | 00:15:00 | ||
| Martingales II | 00:15:00 | ||
| Additional materials Martingale convergence theorem | 00:15:00 | ||
| Module 02 | |||
| Martigales concentration inequality | 00:10:00 | ||
| Talagrand’s concentration | 00:20:00 | ||
| Ito calculus | 00:10:00 | ||
| Ito construction | 00:12:00 | ||
| Ito integral | 00:15:00 | ||
| Ito process and formula | 00:10:00 | ||
| Ito applications | 00:15:00 | ||
| Weak convergence | 00:15:00 | ||
| Tightness of measures | 00:20:00 | ||
| Reflected Brownian motion | 00:10:00 | ||
| Assessment | |||
| Submit Your Assignment | 00:00:00 | ||
| Certification | 00:00:00 | ||
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