Recently we uploaded the paper

- Josef Dick, Daniel Rudolf and Houying Zhu, Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo. ArXiv, 19 March 2013. Submitted, 2013.

In a sense, this paper is an extension of the paper

- Su Chen, Josef Dick, Art Owen, Consistency of Markov Chain quasi-Monte Carlo for continuous state spaces. Ann. Stat., 39, 679–701, 2011. For a blog entry and preprint version see here.

In this paper we prove bounds on the discrepancy of Markov chains which are generated by a deterministic driver sequence . We also prove a Koksma-Hlawka inequality. The main assumption which we use is uniform ergodicity of the transition (Markov) kernel. We describe the essential ingredients and results in the following. Continue reading