Precise asymptotics for large deviations of integral forms

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