A Sample Path Large Deviation Principle for a Class of Population Processes

William H. Sandholm, Mathias Staudigl

Published 2015-11-24Version 1

We establish a sample path large deviation principle for sequences of Markov chains arising in game theory and other applications. As the state spaces of these Markov chains are discrete grids in the simplex, our analysis must account for the fact that the processes run on a set with a boundary. A key step in the analysis establishes joint continuity properties of the state-dependent Cram\'er transform $L(\cdot, \cdot)$, the running cost appearing in the large deviation principle rate function.