Approximation Complexity of Additive Random Fields

Mihail A. Lifshits (1) , Marguerite Zani (2)

1 SPbU - St Petersburg State University
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

Let X (t), t ∈ [0, 1]d be an additive random field. We investigate the complexity of finite rank approximation n X (t, ω) ≈ ) ξk (ω)ϕk (t). k=1 The results obtained in asymptotic setting d → ∞, as suggested H.Wo'zniakowski, provide quantitative version of dimension curse phe- nomenon: we show that the number of terms in the series needed to obtain a given relative approximation error depends on d exponentially and find the explosion coefficients.

Domaines: Probabilités [math.PR]

Mihail A. Lifshits, Marguerite Zani. Approximation Complexity of Additive Random Fields. Journal of Complexity, 2008, 24 (3), pp.362--379. ⟨hal-00796311⟩