An introduction to the theory of self-similar stochastic processes

Self-similar processes such as fractional Brownian motion are stochastic pr ocesses that are invariant in distribution under suitable scaling of time a nd space. These processes can typically be used to model random phenomena w ith long-range dependence. Naturally, these processes are closely related t o the notion of renormalization in statistical and high energy physics. The y are also increasingly important in many other fields of application, as t here are economics and finance. This paper starts with some basic aspects o n selfsimilar processes and discusses several topics from the point of view of probability theory.