Entry requirements

120 credits including 90 credits in mathematics. Participation in Integration Theory and Probability Theory II. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

On completion of the course, the student should be able to:

• use the theory of martingales and martingale transforms in continuous-time ;
• construct Poisson processes on general spaces, and derive Lévy processes and stable processes;
• construct probability measures on infinite dimensional spaces, in particular function spaces;
• effectively compute conditional expectations for continuous stochastic processes and explain the main ideas of the proofs;
• use measure-theoretic and analytic techniques for the derivation of equations describing Markov processes and diffusion processes;
• apply stochastic calculus to study solutions of stochastic differential equations;
• solve partial differential equations by means of Brownian motion and potential theory;
• effectively use the theory of martingales and compensators to derive limits of stochastic systems;
• give examples of applications of stochastic processes and compute invariant measures.

Content

Martingale processes in continuous-time, stochastic Poisson measures, point processes and Lévy processes,  Markov processes and their infinitesimal generators, Brownian motion and diffusion processes, stochastic calculus and stochastic differential equations.

Instruction

Lectures and problem solving lessons.

Assessment

The assessment will be based on individual projects at the end of the course. Compulsory assignments will be given during the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.