Approximation Complexity of Additive Random Fields ... - Google Sites
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Approximation Complexity of Additive Random Fields ... - Google Sites
Approximation Complexity of Additive Random Fields Mikhail Lifshits and Marguerite Zani Let X(t, ω), (t, ω) ∈ [0, 1]d × Ω be an additive random field. We investigate the complexity of finite rank approximation X(t, ω) ≈
n X
ξk (ω)ϕk (t).
k=1
The results obtained in asymptotic setting d → ∞, as suggested H.Wo´zniakowski, provide quantitative version of dimension curse phenomenon: we show that the number of terms in the series needed to obtain a given relative approximation error depends exponentially on d and find the explosion coefficients.
