Linear systems with fractional Brownian motion and Gaussian noise

Methods are presented for calculating the evolution in time of the second moment properties of the output of linear systems subjected to fractional Brownian motion and fractional Gaussian noise, defined as the formal derivative of fractional Brownian motion. The study also examines whether the output of linear systems to fractional Brownian motion and fractional Gaussian noise exhibits long range dependence. Numerical examples are presented to illustrate the calculation of output statistics for some linear systems with fractional Brownian motion and fractional Gaussian noise input, and show that output of linear systems to these input processes may not have long memory.