AVERAGE APPROXIMATION OF TENSOR PRODUCT-TYPE RANDOM FIELDS OF INCREASING DIMENSION

摘要

Consider a sequence of random fields X_d,d ∈ N, given by X_d(t) =∑_(k∈N~d) Π~d_(l=1) λ(k_l)ξ_k Π~d_(l=1)φk_1 (t_1), t ∈ [0, 1]~d, where (λ(i))_(i∈N) ∈l_2, (φ_i)_(i∈N) is an orthonormal system in L_2[0,1], and (ξ_k)_(k∈N~d) are noncorrelated random variables with zero mean and unit variance. We study the exact asymptotic behavior of average-case complexity of approximation to X_d by n-term partial sums providing a fixed level of relative error as d → ∞. The result depends on the existence of a lattice structure of(λ(i))_(i∈N).