# Tag Archives: discrepancy theory

## Digital Nets and Sequences Preprint

A complete preprint of the book

is now available here. The final published version can be obtained directly from Cambridge University Press here.

The preprint version differs of course from the final version, for instance, the page numbers are different. However, the numbering of Chapters, Sections, Theorems, Lemmas, Corollaries, Definitions and Examples is the same in both versions. The list of corrections is for the published version. We do not have a separate list for the preprint version (though the corrections for the published version also apply to the preprint version).

In this paper we prove bounds on the discrepancy of Markov chains which are generated by a deterministic driver sequence $u_1, u_2, \ldots, u_n \in [0,1]^s$. 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