Large time and small noise asymptotic results for mean reverting diffusionprocesses with applications

We use the theory of large deviations to investigate the large time behavio r and the small noise asymptotics of random economic processes whose evolut ions are governed by mean-reverting stochastic differential equations with (i) constant and (ii) state dependent noise terms. We explicitly show that the probability is exponentially small that the time averages of these proc ess will occupy regions distinct from their stable equilibrium position. We also demonstrate that as the noise parameter decreases, there is an expone ntial convergence to the stable position. Applications of large deviation t echniques and public policy implications of our results for regulators are explored.