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

• Measure theory
  
• Weak Convergence
  
• Independent Sums
  
• Dependent Random Variables
  
• Martingales
  
• Stationary Stochastic Processes (we may not get this far)
  

Instructor: Richard Sowers
Office: 347 Illini Hall
Phone: (217) 333-6246
email: r-sowers@math.uiuc.edu
Home page: http://www.math.uiuc.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