Difference between revisions of "Math 544: Advanced Probability 2"
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Revision as of 16:06, 17 July 2010
Contents
Catalog Information
Title
Advanced Probability 2.
Credit Hours
3
Prerequisite
Recommended
Math 341, 342, Stat 441(?); or equivalents.
Description
Advanced concepts in modern probability. Convergence theorems and laws of large numbers. Stationary processes and ergodic theorems. Martingales. Diffusion processes and stochastic integration.
Desired Learning Outcomes
Prerequisites
This course has Math 543 as a prerequisite, so it can build on the work done in that class.
Minimal learning outcomes
Outlined below are topics that all successful Math 544 students should understand well. As evidence of that understanding, students should be able to demonstrate mastery of all relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the content of the major theorems, understanding of the ideas in their proofs, and ability to make direct application of those results to related problems.
- Convergence of random variables
- Almost sure
- In probability
- In mean
- In distribution
- Laws of Large Numbers
- Weak Law
- Strong Law
- Stochastic processes
- Ergodic theory
- Stationary processes
- Birkhoff's ergodic theorem
- Mixing
Additional topics
Courses for which this course is prerequisite
None
