ELEC 697: Introduction to Multifractals (1997)


Tuesday, Thursday: 8:50- 10:15 am, Duncan Hall 2014

My office

Duncan Hall 2025,  x 3020. Please, schedule meetings by email.


Cascades are random processes which are constructed appying a multiplicative iteration scheme. Since they are multiscale in nature, they are best fit to model positive long-range-dependent (LRD) data, such as traffic loads. However, being multiplicative cascades possess a multi-fractal structure which describe their dependence structure which is more complex than the second-order LRD.

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.