Precise asymptotics for large deviations of integral forms

Xiangfeng Yang

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arXiv · 1211.5610

Precise asymptotics for large deviations of integral forms

Xiangfeng Yang

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Abstract

For suitable families of locally infinitely divisible Markov processes $\{ξ^{ε}_t\}_{0\leq t\leq T}$ with frequent small jumps depending on a small parameter $ε>0,$ precise asymptotics for large deviations of integral forms $\mathbb{E}^ε[\exp\{ε^{-1}F(ξ^ε)\}]$ 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 $\mathbb{E}^ε[G(ξ^ε)\}]$ for smooth $G.$ Several connections between these large deviation asymptotics and partial integro-differential equations are included as well.

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Xiangfeng Yang. 2012-11-23. Precise asymptotics for large deviations of integral forms. https://arxiv.org/abs/1211.5610

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