Tuan Anh Nguyen

Preprints:

Nguyen, T. A.
Multilevel Picard approximations overcome the curse of dimensionality when approximating semilinear heat equations with gradient-dependent nonlinearities in L^p-sense
arXiv:2410.00203, 2024

Neufeld, A. & Nguyen, T. A.
Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in L^p-sense
arXiv:2409.20431, 2024

Neufeld, A.; Nguyen, T. A. & Wu, S.
Multilevel Picard approximations overcome the curse of dimensionality in the numerical approximation of general semilinear PDEs with gradient-dependent nonlinearities
arXiv:2311.11579, 2023

Neufeld, A.; Nguyen, T. A. & Wu, S.
Deep ReLU neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial integro-differential equations
Revision requested by Analysis and Applications
arXiv:2310.15581, 2023

Hutzenthaler, M. & Nguyen, T. A.
Multilevel Picard approximations for high-dimensional decoupled forward-backward stochastic differential equations
arXiv:2204.08511, 2022

Hutzenthaler, M. & Nguyen, T. A.
A path-dependent stochastic Gronwall inequality and strong convergence rate for stochastic functional differential equations
arXiv:2206.01049, 2022

Hutzenthaler, M.; Jentzen, A.; Kruse, T. & Nguyen, T. A.
Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities
arXiv:2009.02484, 2020
Revision requested by Numerical Methods for Partial Differential Equations

Nguyen, T. A.
A Liouville principle for the random conductance model under degenerate conditions
arXiv:1908.10691, 2019

Accepted papers:

Neufeld, A. & Nguyen, T. A.
Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean--Vlasov stochastic differential equations
Journal of Mathematical Analysis and Applications, 2025, 541, 128661 [DOI]

Neufeld, A. & Nguyen, T. A.
Rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of gradient-dependent semilinear heat equations
Accepted by Communication in Mathematical Sciences
arXiv:2403.09200, 2024

Hutzenthaler, M.; Jentzen, A.; Kruse, T. & Nguyen, T. A.
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
Journal of Numerical Mathematics, 2023, 31, 1-28 [DOI]

Hutzenthaler, M. & Nguyen, T. A.
Multilevel Picard approximations of high-dimensional semilinear partial differential equations with locally monotone coefficient functions
Applied Numerical Mathematics, 2022, 181, 151-175 [DOI]

Hutzenthaler, M.; Kruse, T. & Nguyen, T. A.
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations
Journal of Mathematical Analysis and Applications, 2022, 507, 125761 [DOI]

Hutzenthaler, M. & Nguyen, T. A.
Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms
Journal of Computational and Applied Mathematics, 2022, 412, 114391 [DOI]

Hutzenthaler, M.; Kruse, T. & Nguyen, T. A.
On the speed of convergence of Picard iterations of backward stochastic differential equations
Probability, Uncertainty and Quantitative Risk, 2021, 7, 133-150 [DOI]

Hutzenthaler, M.; Jentzen, A.; Kruse, T. & Nguyen, T. A.
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
SN Partial Differential Equations and Applications, 2020, 1 [DOI]

Hutzenthaler, M.; Jentzen, A.; Kruse, T.; Nguyen, T. A. & von Wurstemberger, P.
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2020, 476, 20190630 [DOI]

Nguyen, T. A.
An L^p-comparison, p1,, on the finite differences of a discrete harmonic function at the boundary of a discrete box
Potential Analysis, 2020, 56, 351-407 [DOI]

Deuschel, J.-D.; Nguyen, T. A. & Slowik, M.
Quenched invariance principles for the random conductance model on a random graph with degenerate ergodic weights
Probability Theory and Related Fields, 2018, 170, 363-386 [DOI]

Thesis:

Nguyen, T. A.
The random conductance model under degenerate conditions
Technical University of Berlin, 2017 [DOI]