Topics in Mathematical Probability.
  MATH 6534
Instructor: Dr. Janos Englander
     Fall 2009
              
                                                                                          Lectures: MWF 01:00AM-01:50PM

Room:  DUAN G1B25

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Course Content:

 

Measure theoretic preliminaries, sums of independent random variables, notions of convergence, characteristic functions, Central Limit Theorem, random walk.

If time permits: conditioning and martingales, Markov chains, and Brownian motion.

 




Course Grading:


100 percent:  Homework



Exams:

No exams, grades based on homework.



HOMEWORK/READING ASSIGNMENTS:
(Numbers refer to the 4th edition draft)

8/28 (Due 9/4):
Read Section 1.1. and do
Ex. 1.4,1.7,1.9,1.10,1.11

9/4 (Due 9/11):
Read Sections 1.2-1.3. and do
Ex. 1.2.3, 1.2.4, 1.2.5, 1.3.9

9/11 (Due 9/18):
Read Section 1.4. Intro only and do
Ex. 1.3.10, 1.3.12, 1.3.16, 1.4.3


9/18 (Due 9/25):
Read Section 1.4. 1,1.4.2,1.4.3 and do
Ex. 1.4.6, 1.4.7, 1.4.8, 1.4.9

9/25 (Due 10/2):
Read Section 1.4.4, 1.5.1, 1.5.2 and do
Ex.  1.4.14, 1.5.1, 1.5.6, 1.5.8


10/2 (Due 10/9):
Read Section 1.5.3 and do
Ex.  1.5.2., 1.5.3, 1.5.7

10/9 (Due 10/16):
Read Section 1.6 and do
Ex.  1.6.1., 1.6.4, 1.6.10


10/23 (Due 10/30):
Read Section 1.7 and do
Ex.  1.7.1, 1.7.2, 1.7.3

10/30 (Due 11/06):
Read Section 1.8 and do
Ex.  1.8.1, 1.8.2, 1.8.3


11/13 (Due 11/20):
Read Section 1.8 and do
Ex.  2.2.9, 2.2.11,

and prove that in Example 2.2.6, the term V_{n+1} tends to 1/2 a.s.



  The required text for this course is

Probability: Theory and Examples (Probability: Theory & Examples) by Richard Durrett


Note, that there is a link to the errata of the 3rd edition, and to the PDF file of the 4th edition on Prof. Durrett's web page:

http://www.math.cornell.edu/~durrett/PTE/pte.html

It's important you have this book because:

  • There will be required reading from the book
  • Homework assignments will come from the book
  • It will help you get a better grade in my course


                  !!! The option for a final meeting is still open -- please talk to me if interested!!!



 

How to reach me:

Office: MATH 324.
Phone
:
303-492-4846 (with voice mail)
electronic mail

Office Hours:    M,F 11:00-12:00

Enrollment questions: Please see the Registrar's web page, or call their office. If you still have problems, then see Tiffany at the Math. Dept. Office




    

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