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).
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