Probabilistic Adaptive Width of a Multivariate Sobolev Space Equipped with a Gaussian Measure

摘要

In this paper, we determine the asymptotic values of the probabilistic adaptive widths of the space of multivariate functions with bounded mixed derivative (MW2 r(Td),μ) relative to the manifold (YN,ν) in the Lq(Td)-norm, 1 < q ≤ 2, where μ and ν are two given Gaussian measures.