The quadratic variation of Gaussian processes plays an important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this article we study the convergence of quadratic sums of general Gaussian sequences. We provide necessary and sufficient conditions for different types of convergence including convergence in probability, almost sure convergence, $L^{p}$-convergence as well as weak convergence. We use a practical and simple approach which simplifies the existing methodology considerably. As an application, we show how convergence of the quadratic variation of a given process can be obtained by an appropriate choice of the underlying sequence.
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机译：高斯过程的二次变化在随机分析和模型参数估计等应用中都起着重要作用，因此，该主题已在文献中得到了广泛研究。在本文中，我们研究了一般高斯序列的平方和的收敛性。我们为不同类型的收敛提供了必要和充分的条件，包括概率收敛，几乎确定的收敛，$ L ^ {p} $收敛以及弱收敛。我们使用一种实用且简单的方法，大大简化了现有方法。作为应用，我们显示了如何在给定过程的二次变化的收敛可以通过基础序列的适当选择而获得。
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