Theory of Probability, I

Gaussian Distribution
Math 451, Spring 2004

The modern understanding of probability theory is due to Kolmogorov, who in 1933 provided a measure-theoretic foundation for probability which is now treated as axiomatic.  It provides a means of modelling and analyzing both discrete and continuous random variables and processes.    The goal of this course is a fairly rigorous understanding of this framework and its basic implications.  The material in this course is fundamental not only in abstract probabilistic analysis, but also in a number of applied areas such as communications theory, queueing theory, and mathematical finance.  As an organizing goal, we shall attempt to cover Chapters 1 through 6 of Varadhan's fairly recent book Probability Theory (AMS, 2001).   Namely, we shall cover

Prerequisite: The material in Math 441 (measure theory) is a prerequisite for this course.
Grading: Grades will be determined on the basis of homework (30%), a midterm (30%) and a final (40%).
Text: S. R. S. Varadhan: Probability Theory, American Mathematical Society, 2001

Instructor: Richard Sowers
Office: 347 Illini Hall
Phone: (217) 333-6246
email: r-sowers@math.uiuc.edu
Home page: https://faculty.math.illinois.edu/~r-sowers
Class meets: Mondays, Wednesdays, and Fridays 3-3:50 P.M. in 347 Altgeld Hall
Office Hours: Mondays, Wednesdays, and Fridays 12-12:50 P.M. in 347 Illini Hall

killed Brownian Motion