Math 561, CRN 38173, Section E1
Theory of Probability I
This is the first half of the basic graduate course in probability theory.
The goal of this course is to understand the basic tools and language of modern
nprobability theory (see also the
Course Catalog Entry for Math 451 or the list of UIUC
Probability Theory Classes). While I do not wish to sound discouraging, this will be an honest course.
When you finish, you will feel comfortable with the ``plumbing''
of modern probability.
- Introduction and probabilistic framework
Information, Independence, and Conditioning
- Connections with measure theory
- Convergence of random variables
- convergence in L-p
- convergence in probability
- convergence in distribution
Asymptotics: limit theorems
- Sigma-algebra manipulation
- The calculus of sigma-algebras
- Stopping times
- The weak law of large numbers for square-integrable
- Large deviations
- Central Limit Theorem
- Optional Sampling
- Maximal Inequalities
- Crossing Lemmas
- Doob-Meyer Decomposition
Construction of Wiener Measure
- Weak convergence and the Prohorov metric
- The topology of measure space
- Additional References:
- D. Stroock, Probability Theory: an Analytic View, Cambridge University Press, 1993
- H. Royden, Real Analysis, McMillan, 1968
be determined on the basis of homework (30%), a midterm (30%) and a
Department of Mathematics
University of Illinois
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