9 papers
Universal -approximation using median digital-net algorithms
Ziyang Ye, Xiaoqun Wang, Zexin Pan
The paper introduces a median digital‑net algorithm that approximates non‑periodic functions on the unit cube in the L2 norm by estimating Walsh coefficients from randomized sample…
Quasi-Monte Carlo for SDE Simulation: Error Analysis and Dimensionality Reduction
Du Ouyang, Zexin Pan, Zhijian He
We investigate the numerical simulation of general stochastic differential equations (SDEs) using Quasi-Monte Carlo (QMC) methods. First, we provide a rigorous theoretical analysis…
Worst-case -approximation of periodic functions using median lattice algorithms
Zexin Pan, Mou Cai, Josef Dick +2
We study the worst-case approximation of multivariate periodic functions from the weighted Korobov space with smoothness in the Lebesgue norm …
Uncertainty quantification using importance-sampled quasi-Monte Carlo with dimension-independent convergence rates
Zexin Pan, Du Ouyang, Zhijian He
Quasi-Monte Carlo (QMC) integration over unbounded domains remains challenging due to the high dimensionality of sampling space and the boundary growth of the integr…
Quasi-Monte Carlo confidence intervals using quantiles of randomized nets
Zexin Pan
Recent advances in quasi-Monte Carlo integration have shown that for linearly scrambled digital net estimators, the convergence rate can be dramatically improved by taking the medi…
Dimension-independent convergence rates of randomized nets using median-of-means
Zexin Pan
Recent advances in quasi-Monte Carlo integration demonstrate that the median of linearly scrambled digital net estimators achieves near-optimal convergence rates for high-dimension…