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The generalization of fractional Brownian motion in infinite-dimensionalwhite and grey noise spaces has been recently carried over, following theMandelbrot-Van Ness representation, through Riemann-Liouville type fractionaloperators. Our aim is to extend this construction by means of generalfractional derivatives and integrals, which we define through Bernsteinfunctions. According to the conditions satisfied by the latter, some propertiesof these processes (such as continuity, local times, variance asymptotics andpersistence) are derived. On the other hand, they are proved to display short-or long-range dependence, if obtained by means of a derivative or an integral,respectively, regardless of the Bernstein function chosen. Moreover, this kindof construction allows us to define the corresponding noise and to derive anOrnstein-Uhlenbeck type process, as solution of an integral equation.

A class of infinite-dimensional Gaussian processes defined through generalized fractional operators