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 subfractional Brownian motion.

中文翻译：

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从独特的泊松过程向两个独立的高斯过程的收敛趋弱

我们考虑两个独立的高斯过程，它们接受相对于标准Wiener过程的确定性核的随机积分表示。在本文中，我们构造了两个过程族，从唯一的泊松过程（其有限维分布在法律上收敛）到两个独立的高斯过程的有限维分布。作为此结果的应用，我们获得了收敛的过程族在法律上倾向于分数布朗运动和次分数布朗运动。