An Introduction to the Theory of Self-Similar Stochastic Processes

on the occasion of his 70th birthday Selfsimilar processes such as fractional Brownian motion are stochastic processes that are invariant in distribution under suitable scaling of time and space. These processes can typically be used to model random phenomena with long-range dependence. Naturally, these processes are closely related to the notion of renormalization in statistical and high energy physics. They are also increasingly impor-tant in many other elds of application, as there are economics and nance. This paper starts with some basic aspects on selfsimilar pro-cesses and discusses several topics from the point of view of probability theory. Contents and key words 1 Selfsimilarity and long-range dependence | denition of selfsimilarity, existence of exponent of selfsimilarity, long-range dependence