Probabilistic Adaptive Width of a
Multivariate Sobolev Space Equipped with a Gaussian Measure |
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| Authors: | Chen Guanggui Fang Gensun |
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| Institution: | (1) School of Computers and Mathematical-Physical Science, Xihua University, Chengdu 611930, China;(2) School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China |
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| Abstract: | In this paper, we determine the asymptotic values of the probabilistic adaptive widths of the space of multivariate functions
with bounded mixed derivative (MW2r(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. |
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| Keywords: | Probabilistic adaptive width Average adaptive width Sobolev space with bounded mixed derivative Gaussian measure |
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