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Approximation complexity of sums of random processes. / Khartov, A.A.; Zani, M.
в: Journal of Complexity, Том 54, 101399, 10.2019.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Approximation complexity of sums of random processes
AU - Khartov, A.A.
AU - Zani, M.
PY - 2019/10
Y1 - 2019/10
N2 - We study approximation properties of additive random fields Y d(t),t∈[0,1] d, d∈N, which are sums of d uncorrelated zero-mean random processes with continuous covariance functions. The average case approximation complexity n Y d (ε) 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 ε∈(0,1). We investigate the growth of n Y d (ε) for arbitrary fixed ε∈(0,1) and d→∞. The results are applied to the sums of the Wiener processes with different variance parameters.
AB - We study approximation properties of additive random fields Y d(t),t∈[0,1] d, d∈N, which are sums of d uncorrelated zero-mean random processes with continuous covariance functions. The average case approximation complexity n Y d (ε) 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 ε∈(0,1). We investigate the growth of n Y d (ε) for arbitrary fixed ε∈(0,1) and d→∞. The results are applied to the sums of the Wiener processes with different variance parameters.
KW - Additive random fields
KW - Asymptotic analysis
KW - Average case approximation complexity
KW - Wiener process
UR - http://www.scopus.com/inward/record.url?scp=85062453442&partnerID=8YFLogxK
U2 - 10.1016/j.jco.2019.02.002
DO - 10.1016/j.jco.2019.02.002
M3 - Article
VL - 54
JO - Journal of Complexity
JF - Journal of Complexity
SN - 0885-064X
M1 - 101399
ER -
ID: 42683137