Course in Probability Theory, fall 2007

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Level: Graduate Course
 
Credits: 7.5 ECTS credits

Literature:
Durrett, Richard: Probability: Theory and Examples, 3rd edition, Thomson Brooks/Cole, 2004.
(ISBN-10: 0534424414, ISBN-13: 9780534424411).

In case you have the 2nd edition of Durrett's book (Duxbury Press, 1995), you may use it plus the
errata list found at Durrett's home page http://www.math.cornell.edu/~durrett/.
A few details have been added to some proofs in the 3rd edition.

Contents:
We cover about half the contents in Durrett's book, including

Measure theoretic background
Random variables, expectation and independence
Weak Law of Large Numbers
Borel Cantelli Lemmas
Strong Law of Large Numbers
Weak Convergence
Characteristic Functions
Central Limit Theorems for i.i.d. sequences and triangular arrays
Poisson convergence

Course requirements:
To pass, each student has to give one lecture (45 minutes) and solve exercises from three home assignments
distributed during the course. It is also possible to just give the lecture (3 ECTS credits) or just solve the
home assignments (4.5 ECTS credits).
Please inform me if you want to give a lecture, and I will add you to the list of speakers. The two students giving the
lectures a certain week should divide the material between them (see weekly schedule below).

Schedule and registration:
We meet once a week on Mondays 10.15-12.00 at room 306, house 6, Kräftriket, starting on August 27
and finishing on October 22. Please send an email to me (ola@math.su.se) if you wish to attend the course.

Course material:
Weekly schedule
Reading Guide
Home assignment 1 (latest day of return September 17)
Home assignment 2 (latest day of return October 8)
Home assignment 3 (latest day of return October 29)

Welcomce!
Ola Hössjer
Dept. of Mathematics
S-106 91 Stockholm