Abstract Let be zero mean, mean-square continuous, stationary, Gaussian random field with covariance function and let such that G is square integrable with respect to the standard Gaussian measure and is of Hermite rank d. The Breuer-Major theorem in it’s continuous setting gives that, if then the finite dimensional distributions of converge to that of a scaled Brownian motion as Here we give a proof for the case when is a random vector field. We also give a proof for the functional convergence in of Zs to hold under the condition that for some p > 2, where γm denotes the standard Gaussian measure on and we derive expressions for the asymptotic variance of the second chaos component in the Wiener chaos expansion of

中文翻译：

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向量值域的连续 Breuer-Major 定理

摘要 设 为零均值、均方连续、平稳、具有协方差函数的高斯随机场，且令 G 是关于标准高斯测度的平方可积且为 Hermite 秩 d。Breuer-Major 定理在它的连续设置中给出，如果那么 的有限维分布收敛到缩放布朗运动的分布如下 这里我们给出了一个随机向量场的情况的证明。我们还证明了 Zs 的函数收敛在某些 p > 2 的条件下成立，其中 γm 表示标准高斯测度，我们推导出维纳混沌展开中第二个混沌分量的渐近方差的表达式的