ABSTRACT
The theory of large deviations the authors have developed to this point concerns the behavior of a process over fixed time intervals. The Freidlin-Wentzell theory takes these theorems and bootstraps them into estimates on the behavior of a process over very long time intervals, by splitting time into finite intervals and exploiting the Markov property. The authors prove that their main lemma for the Freidlin-Wentzell theory. While the exit problem is interesting and useful, the reasoning behind the theorems is much more general. The chapter examines the reasoning in detail in order to define a more general class of events for which the Freidlin-Wentzell theory holds. Unfortunately, the Freidlin-Wentzell theory is technical, and even more unfortunately, some of the most important things to learn aren’t the theorems, but the techniques brought forth in the proofs.
