2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141457In this paper we present a general mathematical construction that allows us to define a parametric class of $H$-sssi stochastic processes (self-similar with stationary increments), which have marginal probability density function that evolves in time according to a partial integro-differential equation of fractional type. This construction is based on the theory of finite measures on functional spaces. Since the variance evolves in time as a power function, these $H$-sssi processes naturally provide models for slow and fast anomalous diffusion. Such a class includes, as particular cases, fractional Brownian motion, grey Brownian motion and Brownian motion.14 pages, 1 figure, Presented at GF07: Linear and Non-linear Theory of Generalized Functions and Its Applications, The Banach center Bedlewo, Poland, Seprember 2-8 2007ProbabilityMathematical Physics26A33; 33E12; 44A10;33C60; 44A10, 45K05; 60G18text