Micropulses and different types of Brownian motion

Abstract

In this paper we study sums of micropulses that generate different kinds of processes. Fractional Brownian motion and bifractional Brownian motion are obtained as limit processes. Moreover, we not only prove the convergence of finite-dimensional laws but also, in some cases, convergence in distribution in the space of right-continuous functions with left limits. Finally, we obtain generalizations with multidimensional indices.