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Approximation complexity of sums of random processes
Journal of Complexity ( IF 1.8 ) Pub Date : 2019-02-28 , DOI: 10.1016/j.jco.2019.02.002
A.A. Khartov , M. Zani

We study approximation properties of additive random fields Yd(t),t[0,1]d, dN, which are sums of d uncorrelated zero-mean random processes with continuous covariance functions. The average case approximation complexity nYd(ε) is defined as the minimal number of evaluations of arbitrary linear functionals needed to approximate Yd, with relative 2-average error not exceeding a given threshold ε(0,1). We investigate the growth of nYd(ε) for arbitrary fixed ε(0,1) and d. The results are applied to the sums of the Wiener processes with different variance parameters.



中文翻译:

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 ÿdŤŤ[01个]ddñ,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ñÿdε 定义为近似值所需的任意线性泛函的最小求值数 ÿd,相对2平均误差不超过给定阈值 ε01个。我们调查了ñÿdε 对于任意固定 ε01个d。将结果应用于具有不同方差参数的维纳过程的总和。

更新日期:2019-02-28
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