Parabolic Differential Equations

5 credits

Syllabus, Master's level, 1MA055

This course has been discontinued.

A revised version of the syllabus is available.

Code: 1MA055
Education cycle: Second cycle
Main field(s) of study and in-depth level: Mathematics A1F
Grading system: Pass with distinction (5), Pass with credit (4), Pass (3), Fail (U)
Finalised by: The Faculty Board of Science and Technology, 15 March 2007
Responsible department: Department of Mathematics

What is a course syllabus?

Entry requirements

BSc, Introduction to Partial Differential Equations

Learning outcomes

In order to pass the course (grade 3) the student should

know existence and regularity results for parabolic PDEs;

know the Ito-integral and how to use stochastic differential calculus;

know existence and uniqueness theorems for stochastic differential equations;

know how to use Feynman–Kac's representation formula;

be able to apply the theory to optimal stopping problems, free boundary problems, stochastic control theory, and to problems within financial theory.

Content

Existence and regularity theory for parabolic PDEs. Stochastic calculus and diffusion processes. Optimal stopping time problems and free boundary problems. Integro-differential equations.

Instruction

Lectures and problem solving sessions.

Assessment

Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.