Instructor: John Gemmer Office: Manchester #388
E-mail: gemmerj@wfu.edu Office Hours: Tuesday 10-11, Wednesday 2-4, Thursday 1-3
Lecture: MWF: 11:00-11:50, Kirby, Room 10
Textbooks: See syllabus.
Course Handouts:
1. Syllabus: (.pdf)
2. Homework Policy: (.pdf)
3. Example Homework Solutions: (.pdf)
4. Matlab Guide (.pdf)
Matlab Code:
1. Uniform Distribution (UniformSim.m)
2. Emperical Mean of Uniform Distribution (MeanUniform.m)
3. Realizations of Brownian Motion (BrownianMotion1d.m)
4. Density of Brownian Motion (BrownianMotionDensity.m)
5. Realizations of Brownian Motion with Drift (BrownianMotionDrift.m)
6. Density of Brownian Motion with Drift (BrownianMotionDriftDensity.m)
7. Realizations of Brownian Bridge (BrownianBridge.m)
8. Density of Brownian Bridge (BrownianBridgeDensity.m)
9. Comparison with Ito Formula (ItoFormula.m)
Exam Solutions:
1. Exam #1 (.pdf)
2. Exam #2 (.pdf)
Homework Assignments:
1. Homework #1 (.pdf), Solutions (.pdf).
2. Homework #2 (.pdf), Solutions (.pdf).
3. Homework #3 (.pdf), Solutions (.pdf).
4. Homework #4 (.pdf), Solutions (.pdf).
5. Homework #5 (.pdf), Solutions (.pdf).
6. Homework #6 (.pdf), Solutions (.pdf).
7. Homework #7 (.pdf), Solutions (.pdf).
8. Homework #8 (.pdf), Solutions (.pdf).
9. Homework #9 (.pdf), Solutions (.pdf).
Lecture Notes:
1. Lecture #1: (Probability Spaces) (.pdf)
2. Lecture #2: (Random Variables) (.pdf)
3. Lecture #3: (Expectation) (.pdf)
4. Lecture #4: (Random Vectors) (.pdf)
5. Lecture #5: (Gaussian Vectors) (.pdf)
6. Lecture #6: (Gaussian Processes) (.pdf)
7. Lecture #7: (Geometric Viewpoint) (.pdf)
8. Lecture #8: (Properties of Brownian Motion) (.pdf)
9. Lecture #9: (Conditional Expectation) (.pdf)
10. Lecture #10: (Conditional Expecation and Sigma Algebras) (.pdf)
11. Lecture #11: (Martingales) (.pdf)
12. Lecture #12: (Stopping times) (.pdf)
13. Lecture #13: (Ito Integral) (.pdf)
14. Lecture #14: (Ito Formula) (.pdf)
15. Lecture #15: (Stochastic Differential Equations) (.pdf)
16. Lecture #16: (Hitting Times) (.pdf)