Course content

The course is an introduction to continuous time stochastic processes and stochastic differential equations. Survey of measure and probability theory. Independence and conditional expectation. Martingales. Continuous time stochastic processes. Brownian motion. The Ito integral and Ito calculus. Stochastic Differential Equations. Diffusions. The Kolmogorov equations. Applications of stochastic modelling.

Learning outcome

1. Knowledge. Review measure and probability theory. Independence and conditional expectation. Martingales. Brownian motion. The Ito integral and Ito calculus. Stochastic Differential Equations. Diffusions. Then Kolmogorov equations. Applications of stochastic modelling. 2. Skills. The students know the theory of stochastic processes and their applications to stochastic models. They master various stochastic techniques such as martingales, Ito integrals etc. 3. Competence. The students are able to participate in scientific discussions and do research related to stochastic processes at an international level, and also be able to participate in interdisciplinary projects involving stochastic processes and stochastic modeling.

Learning methods and activities

Lectures, alternatively guided self-study. The lectures may be given in English. The students should prepare a small report about a topic related to stochastic differential equations not covered in the lectures.

The course will be lectured every second year, next time Fall 2025. If few students attend, the course may be held as a tutored seminar.

Recommended previous knowledge

The course requires basic knowledge in probability theory and and some mathematical maturity. It is advantageous to have taken the course TMA4145 Lineære metoder.

Course materials

Will be announced at the start of the course.