This post is based on the paper
- [CDO] S. Chen, J. Dick, and A. Owen, Consistency of Markov Chain Quasi-Monte Carlo on continuous state spaces, submitted 2009;
and my previous talks on this topic at the UNSW statistic seminar and the Dagstuhl Workshop in 2009. The slides of my talk at Dagstuhl can be found here. I give an illustration of the results rather than rigorous proofs, which can be found in the paper [CDO].
The classical paper on this topic is by [Chentsov 1967]:
N. N. Chentsov, Pseudorandom numbers for modelling Markov chains, Computational Mathematics and Mathematical Physics, 7, 218–2332, 1967.
Further important steps were taken by A. Owen and S. Tribble, see doi: 10.1073/pnas.0409596102 and doi: 10.1214/07-EJS162. Recent papers of interest in this context are also by A. Hinrichs doi:10.1016/j.jco.2009.11.003, and D. Rudolf doi: 10.1016/j.jco.2008.05.005. The slides of the presentations at Dagstuhl of Hinrichs can be found here here and of Rudolf can be found here.
The task is to approximate an integral Continue reading