A new approach to complex-valued fractional Brownian motion via rotating white noise
A Brownian motion of order \(n\) is defined by a probabilistic approach which is different from those of B. Mandelbrot and P. Sainty. This process is constructed in the form of the integral of a complex Gaussian white noise which itself is defined as the product of a Gaussian white noise by a complex white process which takes on values in the set of \(n\)th roots of unity. An Itô-Taylor's lemma of order \(n\) is proved allowing to derive the dynamical equations of the complex Brownian motion moments whereby a generalized Fokker-Planck equation or heat equation of order \(n\) is obtained. The framework is essentially engineering mathematics.
complex-valued fractional Brownian motion
scientific article; zbMATH DE number 1370423