Fractional brownian motions

Abstract

Properties of different models of fractional Brownian motions are discussed in detail. We shall collect here several possible ways of introducing and defining various possible fBms, discuss their properties, find how they are similar, and how they differ. In particular, we shall try to find what mechanisms or details in their definitions make these motions anomalous and whether can the various models be distinguished experimentally. To this aim, the main tool used here will be the autocorrelation function C(t, s), and related to it characteristics: nonmarkovian behaviour and so-called weak ergodicity breaking.