We study the large deviation and its rate function in the framework of current-valued processes. The class of processes we consider are determined by stochastic line integrals of 1-forms on a compact manifold. We obtain an explicit expression of the rate function, which enables us to observe the difference from the rate function which governs the moderate deviation. As a corollary, our result includes the large deviation for empirical laws in the space of currents.
ASJC Scopus subject areas
- Applied Mathematics