Ricerc@Sapienza

One of the aims of our research consists in the definition of non-gaussian noises different from the one related to Mittag-Leffler functions. Based on this, infinitely dimensional measures (on the Schwartz functions space) can be constructed, which reduce, as special case, to the white noise measure.  A further step in the research project can be represented by the generalization of the fractional operator used in the Mandelbrot-van Ness representation of the fractional Brownian motion (and therefore also in the definition of the grey Brownian motion). If, instead of applying the well-known Riemann-Liouville integral, we consider convolution operators with different kernels, we can accordingly produce processes with more general covariance functions, which, only in a special case, reduce to the fractional Brownian motion.