The best known fractal process is Brownian motion which can be constructed through a simple iteration, a property shared by many fractal objects which can be studied analytically. LRD stands simply for the presence of strong auto-correlations even over large time lags. With the example of Internet data traffic it will be developed how self-similarity can be used in modelling, numerically as well as analytically. Multiplicative measures, in short cascades, were introduced by Mandelbrot in 1974 as models for intermittency in turbulence. Cascades can be viewed as generalizing the self-similarity of fBm and providing a class of processes with greater flexibility.
Cascades possess a multi-fractal structure which describe their highly complex dependence structure.
In this course we try to balance an introduction to the mathematical background of fractals and multifractals with applications of theoretical and practical importance, e.g. in Internet traffic modelling and in image processing. Thereby, we will keep things as simple as possible, making the course accessible to a wide audience. 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. The course is fairly distinct of last year's ELEC 697 and does not assume any pre-knowledge on fractals.