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Preprints
, 2026, Erratum to "Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands", http://dx.doi.org/10.48550/arxiv.1007.0842
, 2026, The curse of dimensionality for geometric $L_1$-discrepancies with nonnegative weights, https://arxiv.org/abs/2607.24290v2
, 2026, A Proof of the Novak--Woźniakowski Conjecture: Optimal Polynomial Tractability Exponents for the Inverse Star Discrepancy, https://arxiv.org/abs/2607.23571v2
, 2026, Spherical Cap $L_2$ Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant, http://dx.doi.org/10.48550/arxiv.2604.21340
, 2026, The star discrepancy of a union of randomly digitally shifted Korobov polynomial lattice point sets depends polynomially on the dimension, http://dx.doi.org/10.48550/arxiv.2509.15877
, 2026, On the quasi-uniformity properties of quasi-Monte Carlo point sets and sequences -- Part I: Lattices and Kronecker sequences, http://dx.doi.org/10.48550/arxiv.2502.06202
, 2026, QMC integration based on arbitrary (t,m,s)-nets yields optimal convergence rates on several scales of function spaces, http://dx.doi.org/10.48550/arxiv.2409.12879
, 2025, A lattice algorithm with multiple shifts for function approximation in Korobov spaces, https://arxiv.org/abs/2511.09071v2
, 2025, Bayesian inference calibration of the modulus of elasticity, http://dx.doi.org/10.48550/arxiv.2510.27060
, 2025, A decomposition-based robust training of physics-informed neural networks for nearly incompressible linear elasticity, http://dx.doi.org/10.48550/arxiv.2505.21994
, 2025, Sparse grid approximation of nonlinear SPDEs: The Landau--Lifshitz--Gilbert equation, http://dx.doi.org/10.48550/arxiv.2310.11225
, 2025, A simple modification to mitigate locking in conforming FEM for nearly incompressible elasticity, http://dx.doi.org/10.48550/arxiv.2407.06831
, 2024, Quasi-Monte Carlo sparse grid Galerkin finite element methods for linear elasticity equations with uncertainties, http://dx.doi.org/10.48550/arxiv.2310.06187
, 2024, Time-fractional diffusion equations with randomness, and efficient numerical estimations of expected values, http://dx.doi.org/10.48550/arxiv.2409.00893
, 2024, An $α$-robust and second-order accurate scheme for a subdiffusion equation, http://dx.doi.org/10.48550/arxiv.2401.04946
, 2023, The fast reduced QMC matrix-vector product, http://dx.doi.org/10.48550/arxiv.2305.11645
, 2023, Quasi-Monte Carlo methods for mixture distributions and approximated distributions via piecewise linear interpolation, http://dx.doi.org/10.48550/arxiv.2304.14786
, 2022, Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate, http://dx.doi.org/10.48550/arxiv.2109.11694
, 2020, Toeplitz Monte Carlo, http://dx.doi.org/10.48550/arxiv.2003.03915
, 2020, Stability of lattice rules and polynomial lattice rules constructed by the component-by-component algorithm, http://dx.doi.org/10.48550/arxiv.1912.10651
, 2020, Tractability properties of the discrepancy in Orlicz norms, http://dx.doi.org/10.48550/arxiv.1910.12571
, 2020, Deep Learning Based Unsupervised and Semi-supervised Classification for Keratoconus, http://dx.doi.org/10.48550/arxiv.2001.11653
, 2020, A note on the periodic $L_2$-discrepancy of Korobov's $p$-sets, http://dx.doi.org/10.48550/arxiv.2001.01973
, 2019, Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification, http://dx.doi.org/10.48550/arxiv.1806.04159
, 2018, Richardson extrapolation of polynomial lattice rules, http://dx.doi.org/10.48550/arxiv.1707.03989
, 2018, Digital net properties of a polynomial analogue of Frolov's construction, http://dx.doi.org/10.48550/arxiv.1712.06831
, 2017, On the optimal order of integration in Hermite spaces with finite smoothness, http://dx.doi.org/10.48550/arxiv.1608.06061
, 2017, Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces, http://dx.doi.org/10.48550/arxiv.1407.8311
, 2016, Construction of interlaced polynomial lattice rules for infinitely differentiable functions, http://dx.doi.org/10.48550/arxiv.1602.00793
, 2016, Multilevel higher order Quasi-Monte Carlo Bayesian Estimation, http://dx.doi.org/10.48550/arxiv.1611.08324
, 2016, Lattice based integration algorithms: Kronecker sequences and rank-1 lattices, http://dx.doi.org/10.48550/arxiv.1608.08687
, 2016, Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness, http://dx.doi.org/10.48550/arxiv.1604.08713
, 2016, Computationally Efficient Bayesian Estimation of High Dimensional Copulas with Discrete and Mixed Margins, https://arxiv.org/abs/1608.06174v3
, 2016, Optimal $L_p$-discrepancy bounds for second order digital sequences, http://dx.doi.org/10.48550/arxiv.1601.07281
, 2016, Higher order Quasi-Monte Carlo integration for Bayesian Estimation, http://dx.doi.org/10.48550/arxiv.1602.07363
, 2015, Digital inversive vectors can achieve strong polynomial tractability for the weighted star discrepancy and for multivariate integration, http://dx.doi.org/10.48550/arxiv.1512.06521
, 2015, A Discrepancy Bound for Deterministic Acceptance-Rejection Samplers Beyond $N^{-1/2}$ in Dimension 1, https://arxiv.org/abs/1510.05351v2
, 2015, Multi-level higher order QMC Galerkin discretization for affine parametric operator equations, http://dx.doi.org/10.48550/arxiv.1406.4432
, 2015, Higher order Quasi-Monte Carlo integration for holomorphic, parametric operator equations, http://dx.doi.org/10.48550/arxiv.1409.2180
, 2015, Higher order QMC Galerkin discretization for parametric operator equations, http://dx.doi.org/10.48550/arxiv.1309.4624
, 2015, On a projection-corrected component-by-component construction, https://arxiv.org/abs/1502.04396v2
, 2015, Fast QMC matrix-vector multiplication, http://dx.doi.org/10.48550/arxiv.1501.06286
, 2014, Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo, http://dx.doi.org/10.48550/arxiv.1311.1890
, 2014, Numerical integration in $\log$-Korobov and $\log$-cosine spaces, http://dx.doi.org/10.48550/arxiv.1411.2715
, 2014, Higher Order Quasi Monte-Carlo Integration in Uncertainty Quantification, http://dx.doi.org/10.48550/arxiv.1409.7970
, 2014, Proof Techniques in Quasi-Monte Carlo Theory, http://dx.doi.org/10.48550/arxiv.1403.7334
, 2014, Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling, http://dx.doi.org/10.48550/arxiv.1408.4609
, 2014, Construction of interlaced scrambled polynomial lattice rules of arbitrary high order, http://dx.doi.org/10.48550/arxiv.1301.6441
, 2014, The inverse of the star-discrepancy problem and the generation of pseudo-random numbers, https://arxiv.org/abs/1407.4208v1
, 2014, A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights, http://dx.doi.org/10.48550/arxiv.1404.5497
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