Brownian motion Brownian motion Brownian motion or pedesis (from "leaping") is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the fast-moving molecules in the fluid. This pattern of motion typically alternates random fluctuations in a particle's position inside a fluid sub-domain with a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such fluid there exists no preferential direction of flow as in transport phenomena. More specifically the fluid's overall
Fractional Brownian motion to a smoother motion. It was introduced by . The value of "H" determines what kind of process the "fBm" is: The increment process, "X"("t") = "B"("t"+1) − "B"("t"), is known as fractional Gaussian noise. There is also a generalization of fractional Brownian motion: "n"-th order fractional Brownian motion, abbreviated as n-fBm. n-fBm is a Gaussian, self-similar, non-stationary process whose increments of order "n" are stationary. For "n" = 1, n-fBm is classical fBm. Like the Brownian motion that it generalizes, fractional Brownian motion is named after 19th century biologist Robert Brown; fractional Gaussian noise is named after mathematician Carl