Precise asymptotics for large deviations of integral forms

Abstract

For suitable families of locally infinitely divisible Markov processes {ξ ǫ t } 0≤t≤T with frequent small jumps depending on a small parameter ǫ > 0, precise asymptotics for large deviations of integral forms E ǫ exp{ǫ −1 F (ξ ǫ )} are proved for smooth functionals F. The main ingredient of the proof in this paper is a recent result regarding the asymptotic expansions of the expectations E ǫ [G(ξ ǫ )}] for smooth G. Several connections between these large deviation asymptotics and partial integro-differential equations are included as well.