Geodesic
Asymptotics of average case approximation complexity for tensor products of Euler integrated processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 147-161

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We consider random fields that are tensor products of $d$ Euler integrated processes. 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 $\varepsilon$. In the paper we obtain logarithmic asymptotics of the average case approximation complexity for such random fields for fixed $\varepsilon$ and $d\to\infty$ under rather weak assumptions for the smoothness parameters of the marginal processes. 
@article{ZNSL_2021_505_a8,
     author = {A. A. Kravchenko and A. A. Khartov},
     title = {Asymptotics of average case approximation complexity for tensor products of {Euler} integrated processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {147--161},
     publisher = {mathdoc},
     volume = {505},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a8/}
}
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A. A. Kravchenko; A. A. Khartov. Asymptotics of average case approximation complexity for tensor products of Euler integrated processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 147-161. http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a8/