Some applications of fractional Brownian motion to linear systems (Q2722573)

The paper summarizes some applications of fractional Brownian motion with long range dependence (that is to say with Hurst parameter between \(1/2\) and 1), in contrast to Markovian fractional processes with independent increments. The process is defined, it is pointed out that it is not a submartingale so that the usual stochastic calculus does not apply here, the directional derivative of processes is defined and it is used to define integrals. Applications refer to scalar and multidimensional linear stochastic differential equations: explicit solutions, moment stability and identification of unknown parameters.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00036].