Tag Archives: pseudo random numbers

Consistency of Markov Chain quasi-Monte Carlo for continuous state spaces

This post is based on the paper

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.

1. Introduction

The task is to approximate an integral Continue reading