Fractional Brownian Motion and Related Processes

Abstract

AbstractChapter 1 surveys the basic properties of fractional Brownian motion and related processes. Fractional Brownian motion is the only Gaussian self-similar process with stationary increments. Its applications to various area are now widely recognized. Recently, other Gaussian self-similar processes, connected with the fractional Brownian motion (the bifractional Brownian motion, the subfractional Brownian motion etc.), have been the object of the study in the scientific literature. We discuss the properties of these processes, including the regularity of their sample paths, the stochastic integral representation, the long-range dependence or the existence of their quadratic variations. We also analyze their interconnections.KeywordsBrownian MotionWiener ProcessFractional Brownian MotionQuadratic VariationHurst ParameterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.