A two‐dimensional Markov renewal process

This paper presents an extension to the the Ivanoff–Merzbach renewal process. The Ivanoff–Merzbach process is a natural analogue to the one‐dimensional renewal process. Restricting our attention to two dimensions, the focus of the current paper will be formation of this extension, which we will refer to as a Markov renewal process, as well as simulation, estimation and applications to data sets in ecology and forestry. Copyright © 2010 John Wiley & Sons, Ltd.