MATH3040 Stochastic Calculus 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
Gaussian processes and Paul Levy Construction of Brownian motion. Elements of Malliavin Calculus in Wiener space, Malliavin derivative, Skorokhod integral. Non+anticipative integrands, continuous martingales, Ito formula and Ito-Clarck Ocone representation formula. Change of measure and Girsanov theorem. Stochastic differential equations, weak and strong solutions. Partial differential equations and Feynman-Kac formula. Applications: stochastic filtering, option pricing in mathematical finance, deep learning and AI.
Learning outcomes
Learning outcomes: to empower the students with applicable knowledge of the fundamentals of stochastic calculus and its powerful mathematical tools.
Description of prerequisites
Probability Theory 1and 2. This 2nd part of the stochastic calculus course on stochastic calculus w.r.t. semimartingales is somehow "orthogonal" to the 1st part where martingales were almost absent. You can follow this 2nd part without having passed the 1st part.