Quasi-Monte Carlo, low discrepancy sequences, and ergodic transformations (Q1068505)

Starting from the importance of low discrepancy sequences in the numerical approximation of integrals by quasi-Monte Carlo methods, the author shows how certain low discrepancy sequences may be generated from ergodic transformations. For example, the well-known van der Corput sequence derives from an example of von Neumann and Kakutani. More specially, the van der Corput sequence and other low sequences can be perceived as orbits of ergodic measure preserving transformations constructed on the unit interval by ''splitting and stacking'' techniques. For constructing measure-preserving transformations the author considers a device initially elaborated by von Neumann and Kakutani.