We obtain asymptotic expansions for the large deviation principle (LDP) for continuous time stochastic processes with weakly-dependent increments. As a key example, we show that additive functionals of solutions of stochastic differential equations (SDEs) satisfying Hörmander condition on a d-dimensional compact manifold admit these asymptotic expansions of all orders.

中文翻译：

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大偏差的高阶渐近——第二部分

我们获得了具有弱依赖增量的连续时间随机过程的大偏差原理 (LDP) 的渐近展开。作为一个关键示例，我们展示了满足 Hörmander 条件的随机微分方程 (SDE) 解的加性泛函d维紧流形承认所有阶的这些渐近展开。