Thesis from 2007 in the field of Mathematics - Stochastic, grade: very good, Philipps University Marburg, language: German, abstract: The term "fractal" was coined by Mandelbrot in the 1970s in his book "The Fractal Geometry of Nature." Although there is no precise definition of a "fractal," it has entered our everyday language. The initial interest in the properties of processes on fractals came from mathematical physicists who wondered how, for example, heat or a fluid spreads on fractals. To answer these questions, one needs the theory of "Analysis on Fractals." The spread of heat can be described by the heat equation. However, if the domain of the Laplace operator is a fractal, the problem arises that curves such as the Sierpinski.