Discrepancy Theory and Quasi-Monte Carlo Integration

By Josef Dick, Friedrich Pillichshammer. 2014

99 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Numerical Analysis

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Juan Antonio Cuesta-Albertos
2. Eustasio del Barrio
3. Carlos Matrán
4. Marc Hallin
5. Nicolas Chopin
6. Chris J. Oates
7. Mark A. Girolami

In Numerical Analysis

1. Chris J. Oates
2. Mark A. Girolami
3. Juan Antonio Cuesta-Albertos
4. Eustasio del Barrio
5. Carlos Matrán
6. Marc Hallin
7. Nicolas Chopin
8. Qiang Liu

Citations in the corpus

• Control functionals for Monte Carlo integration (2014, methodology): “Theorem 3 provides an explicit error bound for f ∈H+, mimicking the approach of (R)QMC (Dick and Pillichshammer (2010), section 2.3.3).”
• Distribution and quantile functions, ranks and signs in dimension d: A measure transportation approach (2021, methodology): “…the low-discrepancy sequences of the type considered in numerical integration and Monte-Carlo methods (see, e.g., Niederreiter (1992), Judd (1998), Dick and Pillichshammer (2014), or Santner et al. (2003)), which are current practice in numerical integration and the design of computer experiments.”
• Control Functionals for Quasi-Monte Carlo Integration (2015, methodology): “QMC is naturally studied in reproducing kernel Hilbert spaces (RKHS; [8]).”