fractional Brownian Motion (fBM)

Abstract

Brownian Motion serves as the foundation of a myriad of statistical modelling. Here, we discuss the statistical properties of Weiner processes, and introduce Brownian Motion as a continuous Weiner process. Further, we model it using Langevin and Fokker-Planck equations and study the motion of particles in a 1-D box. This is supplemented by simulations. Further, fractional Brownian Motion is introduced as a generalisation and its statistical properties are studied. Its non-trivial simulation is also done by two methods.