84 citations · 138 across the 17 of their papers we have counts for
17 papers
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…
Foliations Formed by Generic Coadjoint Orbits of Lie Groups Corresponding to a Class Seven-Dimensional Solvable Lie Algebras
Tuyen T. M. Nguyen, Vu A. Le, Tuan A. Nguyen
We consider all connected and simply connected 7-dimensional Lie groups whose Lie algebras have nilradical $\g_{5,2} = \s \{X_1, X_2, X_3, X_4, X_5 \colon [X_1, X_2] = X_4, [X_1, X…
A path-dependent stochastic Gronwall inequality and strong convergence rate for stochastic functional differential equations
Martin Hutzenthaler, Tuan Anh Nguyen
We derive a stochastic Gronwall lemma with suprema over the paths in the upper bound of the assumed affine-linear growth assumption. This allows applications to Itô processes with…
Multilevel Picard approximations for high-dimensional decoupled forward-backward stochastic differential equations
Martin Hutzenthaler, Tuan Anh Nguyen
Backward stochastic differential equations (BSDEs) appear in numeruous applications. Classical approximation methods suffer from the curse of dimensionality and deep learning-based…
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…
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…
Testing isomorphism of complex and real Lie algebras
Tuan A. Nguyen, Vu A. Le, Thieu N. Vo
In this paper, we give algorithms for determining the existence of isomorphism between two finite-dimensional Lie algebras and compute such an isomorphism in the affirrmative case.…
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…
On the problem of classifying solvable Lie algebras having small codimensional derived algebras
Hoa Q. Duong, Vu A. Le, Tuan A. Nguyen +2
This paper concerns the problem of classifying finite-dimensional real solvable Lie algebras whose derived algebras are of codimension 1 or 2. On the one hand, we present an effect…
A Liouville principle for the random conductance model under degenerate conditions
Tuan Anh Nguyen
We consider a random conductance model on the -dimensional lattice, , where the conductances take values in and are however not assume…
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…
On the classifying problem for the class of real solvable Lie algebras having 2-dimensional or 2-codimensional derived ideal
Vu A. Le, Tuan A. Nguyen, Tu T. C. Nguyen +2
Let denote the class of all -dimensional real solvable Lie algebras having -dimensional derived ideal (). In 199…
Quenched invariance principles for the random conductance model on a random graph with degenerate ergodic weights
Jean-Dominique Deuschel, Tuan Anh Nguyen, Martin Slowik
We consider a stationary and ergodic random field that is parameterized by the edge set of the Euclidean lattice , . The random varia…