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20162026
most citedA proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

48 citations · 151 across the 14 of their papers we have counts for

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Showing 2017Show all

2 papers · 1 filter

math.NA2017★ 26 cited

Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations

Arnulf Jentzen, Diyora Salimova, Timo Welti

In this paper we propose and analyze explicit space-time discrete numerical approximations for additive space-time white noise driven stochastic partial differential equations (SPD…

math.NA2017★ 10 cited

On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions

Máté Gerencsér, Arnulf Jentzen, Diyora Salimova

In the recent article [Jentzen, A., Müller-Gronbach, T., and Yaroslavtseva, L., Commun. Math. Sci., 14(6), 1477--1500, 2016] it has been established that for every arbitrarily slow…