84 citations · 138 across the 17 of their papers we have counts for
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Full history recursive multilevel Picard approximations suffer from the curse of dimensionality for the Hamilton-Jacobi-Bellman equation of a stochastic control problem
Martin Hutzenthaler, Tuan Anh Nguyen
Full history recursive multilevel Picard (MLP) approximations have been proved to overcome the curse of dimensionality in the numerical approximation of semilinear heat equations w…
Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functions
Martin Hutzenthaler, Tuan Anh Nguyen
The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only method which provably overcomes the cur…
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…
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…
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse +1
The recently introduced full-history recursive multilevel Picard (MLP) approximation methods have turned out to be quite successful in the numerical approximation of solutions of h…
An -comparison, , on the finite differences of a discrete harmonic function at the boundary of a discrete box
Tuan Anh Nguyen
It is well-known that for a harmonic function defined on the unit ball of the -dimensional Euclidean space, , the tangential and normal component of the gradient $\…
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse +1
Deep neural networks and other deep learning methods have very successfully been applied to the numerical approximation of high-dimensional nonlinear parabolic partial differential…