Brownian web paths from a random space time point. The introduction of this topology allowed them to prove the convergence of the coalescing random walks to a unique limiting object and characterize it. They named this limiting object Brownian web. An extension of the Brownian web, called the Brownian net, has been introduced by Sun and Swart by allowing the coalescing Brownian motions to undergo branching. An alternative construction of the Brownian net was given by Newman, Ravishankar and Schertzer. For a recent survey, see Schertzer, Sun and Swart. Brownian web In probability theory, the Brownian web is an uncountable collection of
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