Stochastic differential equations driven by fractional Brownian motion with Hurst parameter 1/2<H<1 and Young integral

In this work we introduce the fractional Brownian motion with Hurst parameter H>1/2 and its simulation using R, we study the stochastic integral in Young sense and we prove the existence and the uniqueness of the solution of stochastic differential equations driven by the corresponding noise.In this study of long-term storage capacity and design of reservoirs based on investigations of river water levels along the Nile, Hurst observed a phenomenon which is invariant to changes in scale. Such a scale-invariant phenomenon was also observed in studies of problems connected with traffic patterns of packet flows in high-speed data networks such as the Internet.