Induced rare events: analysis via large deviations and time reversal

TLDR: In this paper, the authors apply the notions of reversed time for Markov processes and large deviations for jump-Markov systems to general jump-markov systems and show that the way a constant coefficient process approaches a rare event is roughly by following the path of another constant-coefficient process.

Abstract: When a subsystem goes into an infrequent state, how does the remainder of the system behave? We show how to calculate the relevant distributions using the notions of reversed time for Markov processes and large deviations. For ease of exposition, most of the work deals with a specific queueing model due to Flatto, Hahn, and Wright. However, we show how the theorems may be applied to much more general jump-Markov systems. We also show how the tools of time-reversal and large deviations complement each other to yield general theorems. We show that the way a constant coefficient process approaches a rare event is roughly by following the path of another constant coefficient process. We also obtain some properties, including a priori bounds, for the change of measure associated with some large deviations functionals; these are useful for accelerating simulations.