We study approximation properties of additive random fields $Y_d\left(t\right),t\in {[0,1]}^d$, $d\in \mathbb{N}$, which are sums of $d$ uncorrelated zero-mean random processes with continuous covariance functions. The average case approximation complexity $n^{Y_d}\left(\epsilon \right)$ is defined as the minimal number of evaluations of arbitrary linear functionals needed to approximate $Y_d$, with relative 2-average error not exceeding a given threshold $\epsilon \in (0,1)$. We investigate the growth of $n^{Y_d}\left(\epsilon \right)$ for arbitrary fixed $\epsilon \in (0,1)$ and $d\to \infty$. The results are applied to the sums of the Wiener processes with different variance parameters.

中文翻译：

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随机过程之和的近似复杂度

我们研究加法随机场的近似性质 ${ÿ}_d（Ť），Ť\in {[0，\mathrm{1个}]}^d$， $d\in \mathbb{ñ}$，是 $d$具有连续协方差函数的不相关零均值随机过程。平均案例近似复杂度${ñ}^{{ÿ}_d}（\epsilon ）$ 定义为近似值所需的任意线性泛函的最小求值数 ${ÿ}_d$，相对2平均误差不超过给定阈值 $\epsilon \in （0，\mathrm{1个}）$。我们调查了${ñ}^{{ÿ}_d}（\epsilon ）$ 对于任意固定 $\epsilon \in （0，\mathrm{1个}）$ 和 $d\to \infty$。将结果应用于具有不同方差参数的维纳过程的总和。