Asymptotics of Average Case Approximation Complexity for Tensor Products of Euler Integrated Processes

Random fields that are tensor products of d Euler integrated processes are considered. The average case approximation complexity for a given random field is defined as the minimal number of values of continuous linear functionals that is needed to approximate the field with relative 2-average error not exceeding a given threshold ε. Logarithmic asymptotics of the average case approximation complexity is obtained for such random fields for fixed ε and d → ∞ under rather weak assumptions for the smoothness parameters of the marginal processes.