Markovian diffusive representation of 1/f(alpha) noises and application tofractional stochastic differential models

This paper is devoted to linear stochastic differential systems with fracti onal noise (or fractional Brownian motion) input. On the basis of a conveni ent Markovian description of such noises, elaborated from a diffusive repre sentation of fractional integrators previously introduced in a deterministi c context, the fractional differential system is equivalently transformed i nto a standard (but infinite-dimensional) one, with white-noise input. Fini te-dimensional approximations mag. easily be obtained from classical discre tization schemes. With this equivalent representation, the correlation function of processes described by linear fractional stochastic differential systems may be expre ssed from the solution of standard differential systems, which generalizes, in some way, the well-known differential Lyapunov equation, which appears when computing the covariance matrix associated with standard linear stocha stic systems.