Precise large deviations for Ornstein-Uhlenbeck processes

Abstract

For a family of Ornstein-Uhlenbeck processes having an infinitesimal size of noise, we prove precise asymptotics for large deviations of an integral form over the continuous path space. The main ingredients in the proof are an exponential change of measures and subtle Taylor expansions with suitable estimates. An application of these precise integral large deviations to partial differential equations is included.