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We consider two independent Gaussian processes that admit a representation in terms of a stochastic integral of a deterministic kernel with respect to a standard Wiener process. In this paper we construct two families of processes, from a unique Poisson process, the finite dimensional distributions of which converge in law towards the finite dimensional distributions of the two independent Gaussian processes. As an application of this result we obtain families of processes that converge in law towards fractional Brownian motion and sub-fractional Brownian motion., Comment: 11 pages

If X is a finite set of points in a multiprojective space P^n1 x ... x P^nr with r >= 2, then X may or may not be arithmetically Cohen-Macaulay (ACM). For sets of points in P^1 x P^1 there are several classifications of the ACM sets of points. In this paper we investigate the natural generalizations of these classifications to an arbitrary multiprojective space. We show that each classification for ACM points in P^1 x P^1 fails to extend to the general case. We also give some new necessary and sufficient conditions for a set of points to be ACM., 21 pages; revised final version; minor corrections; to appear in Collectanea Mathematica