443 citations · 2.4k across the 59 of their papers we have counts for
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Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions
Martin Hutzenthaler, Arnulf Jentzen, Katharina Pohl +2
In many numerical simulations stochastic gradient descent (SGD) type optimization methods perform very effectively in the training of deep neural networks (DNNs) but till this day…
Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms
Tuan Anh Nguyen, Martin Hutzenthaler
Classical approximation results for stochastic differential equations analyze the -distance between the exact solution and its Euler-Maruyama approximations. In this article w…
Strong -error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations
Martin Hutzenthaler, Arnulf Jentzen, Benno Kuckuck +1
Full-history recursive multilevel Picard (MLP) approximation schemes have been shown to overcome the curse of dimensionality in the numerical approximation of high-dimensional semi…
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse +1
Backward stochastic differential equations (BSDEs) belong nowadays to the most frequently studied equations in stochastic analysis and computational stochastics. BSDEs in applicati…
On the speed of convergence of Picard iterations of backward stochastic differential equations
Martin Hutzenthaler, Thomas Kruse, Tuan Anh Nguyen
It is a well-established fact in the scientific literature that Picard iterations of backward stochastic differential equations with globally Lipschitz continuous nonlinearity conv…
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations
Martin Hutzenthaler, Thomas Kruse, Tuan Anh Nguyen
In the literatur there exist approximation methods for McKean-Vlasov stochastic differential equations which have a computational effort of order . In this article we introduce…