MATH3020 Probability Theory II (5 cr)
Cooperation network course
Network: Vaasa Higher Education Consortium
Network: Cross-institutional studies in advanced courses in mathematics and statistics
This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Master's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master's Degree Programme in Mathematics (Subject Teacher)
- Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Doctoral Programme in Mathematics and Statistics
- Doctoral Programme in Mathematics and Science (Specialication in Mathematics)
Description
Conditional expectation, regular conditional laws, filtered probability space, martingale, supermartingale and submartingale, predictable processes, martingale transformation, stopping times, uniform integrability, Doob's optional stopping theorem, Doob's martingale convergence theorem
Learning outcomes
The student will have a deep understanding of conditional expectations and martingales
Description of prerequisites
Probability Theory I and Functional Analysis or equivalent knowledge