Quasi-Monte Carlo#

Low-discrepancy points instead of random ones: Halton and Sobol sequences, the Koksma-Hlawka error bound, randomized QMC with error bars, and high-dimensional path integrals with and without the Brownian bridge.

Halton sequences

Halton sequences

Koksma-Hlawka and discrepancy

Koksma-Hlawka and discrepancy

Sobol sequences

Sobol sequences

Owen scrambling: randomized QMC

Owen scrambling: randomized QMC

Paskov-Traub: QMC in high dimension

Paskov-Traub: QMC in high dimension

Caflisch-Moskowitz Brownian bridge

Caflisch-Moskowitz Brownian bridge