This work began as a research paper intended to show how the convergence
of nonlinear semigroups associated with a sequence of Markov processes implied
the large deviation principle for the sequence. We expected the result to be of little
utility for specific applications, since classical convergence results for nonlinear
semigroups involve hypotheses that are very difficult to verify, at least using classical
methods. We should have recognized at the beginning that the modern theory
of viscosity solutions provides the tools needed to overcome the classical difficulties.
Once we did recognize that convergence of the nonlinear semigroups could be
verified, the method evolved into a unified treatment of large deviation results for
Markov processes, and the research “paper” steadily grew into the current volume.