TY - JOUR

T1 - Average approximation of tensor product-type random fields of incresing dimension

AU - Khartov, A.A.

PY - 2013

Y1 - 2013

N2 - Consider a sequence of ramdom fields Xd, d ∈ ℕ, given by, where (λ(i))i∈ℕ ∈l2 is an orthonormal system in L2[0,1], and (ξk)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 Xd 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. Bibliography: 9 titles. © 2013 Springer Science+Business Media New York.

AB - Consider a sequence of ramdom fields Xd, d ∈ ℕ, given by, where (λ(i))i∈ℕ ∈l2 is an orthonormal system in L2[0,1], and (ξk)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 Xd 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. Bibliography: 9 titles. © 2013 Springer Science+Business Media New York.

U2 - 10.1007/s10958-013-1170-7

DO - 10.1007/s10958-013-1170-7

M3 - Article

SP - 769

EP - 782

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -