Advanced Stochastic Processes | Sloan School of Management | MIT OpenCourseWare

Course Info

Instructor

Prof. David Gamarnik

Departments

As Taught In

Fall 2013

Level

Graduate

Topics

Mathematics
- Probability and Statistics

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Lecture Notes

Instructor Insights

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Lecture Notes

Additional materials: Martingales convergence theorem

Lecture 1: Metric spaces

Lecture 2: Large deviations technique

Lecture 3: Cramer's theorem

Lecture 4: Applications of large deviations

Lecture 5: LD in many dimensions and Markov chains

Lecture 6: Intro brownian motion

Lecture 7: Brownian motion

Lecture 8: Quadratic variation

Lecture 9: Filteration and martingales

Lecture 10: Martingales I

Lecture 11: Martingales II

Lecture 12: Martingales concentration inequality

Lecture 13: Talagrand's concentration inequality

Lecture 14: Ito calculus

Lecture 15: Ito construction

Lecture 16: Ito integral

Lecture 17: Ito process and formula

Lecture 19: Ito applications

Lecture 20: Weak convergence

Lecture 21: Tightness of measures

Lecture 22: Reflected brownian motion

Course Info

Instructor

Prof. David Gamarnik

Departments

As Taught In

Fall 2013

Level

Graduate

Topics

Mathematics
- Probability and Statistics

Learning Resource Types

Lecture Notes

Instructor Insights

Problem Sets

Problem Set Solutions

Exams

Exam Solutions

Download Course

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