An introduction to the theory of self-similar stochastic processes

Self-similar 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 important in many other fields of application, as there are economics and finance. This paper starts with some basic aspects on selfsimilar processes and discusses several topics from the point of view of probability theory.