A Note on Monotone Markov Processes

This note contains some technical results developed for Kamihigashi and Stachurski (2010). We first consider a stochastic kernel on an arbitrary measurable space and establish some general results. We then introduce a preorder and consider an increasing stochastic kernel. None of our results requires any topological assumption. To make this note self-contained, we include some of the definitions reviewed or discussed in Kamihigashi and Stachurski (2010).