Bilinear stochastic systems with fractional Brownian motion input

Abstract

The partial derivatives with respect to time and the fractional Brownian motion of a particular class of stationary processes are defined. Although the fractional Brownian motion is not semimartingale, the bilinear SDE with fractional Brownian motion input is considered and solved. The solution is explicitly given in both the frequency and time domains in the case when the coefficient of the bilinear term is pure imaginary. The stationary Stratonovich solution of the bilinear SDE with white noise input is also considered.