LEC #  TOPICS  LECTURE NOTES 

1  Metric spaces and topology  Lecture 1: Metric spaces (PDF) 
2  Large deviations for i.i.d. random variables  Lecture 2: Large deviations technique (PDF) 
3 
Large deviations theory Cramér’s theorem 
Lecture 3: Cramér’s theorem (PDF) 
4  Applications of the large deviations technique  Lecture 4: Applications of large deviations (PDF) 
5 
Extension of LD to ℝ^{d}and dependent process GärtnerEllis theorem 
Lecture 5: LD in many dimensions and Markov chains (PDF) 
6  Introduction to Brownian motion  Lecture 6: Intro Brownian motion (PDF) 
7 
The reflection principle The distribution of the maximum Brownian motion with drift 
Lecture 7: Brownian motion (PDF) 
8  Quadratic variation property of Brownian motion  Lecture 8: Quadratic variation (PDF) 
9  Conditional expectations, filtration and martingales  Lecture 9: Filtration and martingales (PDF) 
10  Martingales and stopping times I  Lecture 10: Martingales I (PDF) 
11 
Martingales and stopping times II Martingale convergence theorem 

12  Martingale concentration inequalities and applications  Lecture 12: Martigales concentration inequality (PDF) 
13  Concentration inequalities and applications  Lecture 13: Talagrand’s concentration inequality (PDF) 
14  Introduction to Ito calculus  Lecture 14: Ito calculus (PDF) 
15  Ito integral for simple processes  Lecture 15: Ito construction (PDF) 
Midterm Exam  
16  Definition and properties of Ito integral  Lecture 16: Ito integral (PDF) 
17 
Ito process Ito formula 
Lecture 17: Ito process and formula (PDF) 
18  Integration with respect to martingales  Notes unavailable 
19  Applications of Ito calculus to financial economics  Lecture 19: Ito applications (PDF) 
20  Introduction to the theory of weak convergence  Lecture 20: Weak convergence (PDF) 
21 
Functional law of large numbers Construction of the Wiener measure 
Lecture 21: Tightness of measures (PDF) 
22 
Skorokhod mapping theorem Reflected Brownian motion 
Lecture 22: Reflected Brownian motion (PDF) 
Final Exam 
Lecture Notes
Course Info
Instructor
As Taught In
Fall
2013
Level
Learning Resource Types
assignment_turned_in
Problem Sets with Solutions
grading
Exams with Solutions
notes
Lecture Notes
Instructor Insights