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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.


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.


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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
Submit Your Assignment 00:00:00
Certification 00:00:00

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