Fractional Brownian Motion

Fractional Brownian motion (fBM) is a mathematical model that describes a type of continuous, random movement, similar to the way particles move in liquids. Unlike traditional Brownian motion, fBM accounts for long-term dependencies, meaning past movements influence future ones, either making the process more persistent (trending) or more erratic. It is characterized by the Hurst parameter, which determines the degree of this dependency. fBM is useful in fields like finance, telecommunications, and physics to model phenomena where past behaviors affect future dynamics over different timescales.