Math 672: Probability Theory II

Cornell University, Spring 2007

MW 11:40-12:55, Malott 206

 

 

Instructor: Prof. Jung, 591 Malott, 255-8268, pjung@math.cornell.edu

Office hours: Tuesday 12:45-2:45, and by appointment on Friday.

 

TA: Zhigen Zhao, 218 Malott, agzhou.math.cornell.edu

Office hours: Wednesday 1-2

 

Grading: Final 35%; HW 65%

 

Homework: Homework should be done daily at the same pace as the lectures.  Homework is the MOST IMORTANT PART of class!  Even if you think you understand the book/lectures you really don’t until you have worked out examples on your own. You may consult other students regarding your homework, but the final write-up should be done on your own (in other words, no copying).

 

Material: Probability: Theory and Examples by Rick Durrett (for Brownian Motion see also Karatzas/Shreve and Brieman)

 

HW #1: Show that for stopping times N_1 less than or equal to N_2, The sigma algebra F_{N_1} is contained in F_{N_2}. Also, problems 5.1.1, 5.1.6, 5.1.7, 5.1.8, 5.2.1, 5.2.6 Due on 2/12

 

HW #2: 5.3.2 (ii), 5.3.4, 5.3.6, 5.3.9 Due 2/21

 

HW #3: 5.4.3, 5.4.6, 5.4.10 (hint: for this one, read Example 4.5) Due 2/28

 

HW #4: 6.1.1, 6.1.3, 6.1.7, 6.2.1, 6.2.2 Due 3/14

 

HW #5: 7.1.3, 7.2.1, 7.2.2, 7.2.3, 7.2.4 Due 4/11

 

HW #6: 7.3.2, 7.3.7, 7.4.1, 7.4.2 Due 4/18

 

HW #7: 7.5.3 (for part (ii) use equation 7.4.4), 7.5.7 (hint: see exercise 7.5.5), 7.6.2, 7.6.3 Due 5/2

Final Exam