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
Wiener process Wiener processes, as before). Generalities: Numerical path sampling: Wiener process In mathematics, the Wiener process is a continuous-time stochastic process named in honor of Norbert Wiener. It is often called standard Brownian motion process or Brownian motion due to its historical connection with the physical process known as Brownian movement or Brownian motion originally observed by Robert Brown. It is one of the best known Lévy processes (càdlàg stochastic processes with stationary independent increments) and occurs frequently in pure and applied mathematics, economics, quantitative finance, evolutionary biology, and physics. The Wiener process plays an important role in both pure and