In this course we start with an introduction to the mathematical background of fractals, iteration and dimensions. With deterministic cascades we then explain the principles of multifractal analysis, in particular its relation to Large Deviations: the multifractal spectrum compactly represents the frequency of rare events, such as bursts in traffic loads, and goes, thus, beyond a global (almost sure) description. We round up the course by a chapter on random cascades.
Homework will be assigned on an irregular basis. Students who wish to claim credit are expected to do a project which may consist of presenting a research article or programming. Only a basic course in probability (ELEC 533) is required.