Select Publications
Preprints
2016, On the optimal order of integration in Hermite spaces with finite smoothness, http://dx.doi.org/10.48550/arxiv.1608.06061
,2016, Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness, http://dx.doi.org/10.48550/arxiv.1604.08713
,2016, Higher order Quasi-Monte Carlo integration for Bayesian Estimation, http://dx.doi.org/10.48550/arxiv.1602.07363
,2016, Construction of interlaced polynomial lattice rules for infinitely differentiable functions, http://dx.doi.org/10.48550/arxiv.1602.00793
,2016, Optimal $L_p$-discrepancy bounds for second order digital sequences, http://dx.doi.org/10.48550/arxiv.1601.07281
,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, Fast QMC matrix-vector multiplication, http://dx.doi.org/10.48550/arxiv.1501.06286
,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, Higher order Quasi-Monte Carlo integration for holomorphic, parametric operator equations, http://dx.doi.org/10.48550/arxiv.1409.2180
,2014, Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling, http://dx.doi.org/10.48550/arxiv.1408.4609
,2014, 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
,2014, Multi-level higher order QMC Galerkin discretization for affine parametric operator equations, http://dx.doi.org/10.48550/arxiv.1406.4432
,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
,2014, The weighted star discrepancy of Korobov's $p$-sets, http://dx.doi.org/10.48550/arxiv.1404.0114
,2014, Proof Techniques in Quasi-Monte Carlo Theory, http://dx.doi.org/10.48550/arxiv.1403.7334
,2013, Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo, http://dx.doi.org/10.48550/arxiv.1311.1890
,2013, Higher order QMC Galerkin discretization for parametric operator equations, http://dx.doi.org/10.48550/arxiv.1309.4624
,2013, Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition, http://dx.doi.org/10.48550/arxiv.1306.2821
,2013, Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high dimensional periodic functions, http://dx.doi.org/10.48550/arxiv.1304.0329
,2013, The decay of the Walsh coefficients of smooth functions, http://dx.doi.org/10.48550/arxiv.1304.1052
,2013, Walsh spaces containing smooth functions and quasi-Monte Carlo rules of arbitrary high order, http://dx.doi.org/10.48550/arxiv.1304.0328
,2013, Construction of interlaced scrambled polynomial lattice rules of arbitrary high order, http://dx.doi.org/10.48550/arxiv.1301.6441
,2012, Approximation of analytic functions in Korobov spaces, http://dx.doi.org/10.48550/arxiv.1211.5822
,2012, Lattice rules for nonperiodic smooth integrands, http://dx.doi.org/10.48550/arxiv.1211.3799
,2012, Infinite-Dimensional Integration in Weighted Hilbert Spaces: Anchored Decompositions, Optimal Deterministic Algorithms, and Higher Order Convergence, http://dx.doi.org/10.48550/arxiv.1210.4223
,2012, A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness, http://dx.doi.org/10.48550/arxiv.1203.5157
,2011, Point sets on the sphere $\mathbb{S}^2$ with small spherical cap discrepancy, http://dx.doi.org/10.48550/arxiv.1109.3265
,2011, Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules, http://dx.doi.org/10.48550/arxiv.1105.2599
,2011, Consistency of Markov chain quasi-Monte Carlo on continuous state spaces, http://dx.doi.org/10.48550/arxiv.1105.1896
,2011, Quasi-Monte Carlo rules for numerical integration over the unit sphere $\mathbb{S}^2$, http://dx.doi.org/10.48550/arxiv.1101.5450
,2011, A simple Proof of Stolarsky's Invariance Principle, http://dx.doi.org/10.48550/arxiv.1101.4448
,2010, 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
,2010, A Construction of Polynomial Lattice Rules with Small Gain Coefficients, http://dx.doi.org/10.48550/arxiv.1003.4785
,2008, A Multivariate Fast Discrete Walsh Transform with an Application to Function Interpolation, http://dx.doi.org/10.48550/arxiv.0808.0487
,Other
2012, A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rules, http://arxiv.org/abs/1207.5275v1
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