The simplification and application on the fractional Brownian motion

In recent years,the fractional Brownian motion,as an extension of the Brownian motion,has attracted more and more attention.Its applications involved many areas,especially the applications in diffusion and dispersion process in river,coastal waters and open seas.Expensive calculations would be involved when simulating large amount of pullutant using particle clouds.Different from Brownian motion,the fractional Brownian motion is related to a long-term memory.Hence,another expensive calcultion would also involved.Our work is to approach Brownian motion using simpler random walks,in order to develop a simplified fractional Brownian motion model.The differences of the original model and simplified models are studied and furthermore,the simplified fractional Brownian motion models are used in simulating the pollutant diffusion and dispersion in coastal waters.