# Higher order asymptotics for large deviations -- Part II

## TL;DR

This paper develops detailed asymptotic expansions for large deviations in continuous-time stochastic processes with weak dependence, including additive functionals of SDEs satisfying Hörmander's condition on compact manifolds.

## Contribution

It provides the first comprehensive asymptotic expansion of all orders for large deviations in this class of stochastic processes.

## Key findings

- Asymptotic expansions are derived for processes with weakly dependent increments.
- Additive functionals of Hörmander SDEs on compact manifolds admit these expansions.
- The results extend large deviation principles to higher-order asymptotics.

## Abstract

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 H\"ormander condition on a $d-$dimensional compact manifold admit these asymptotic expansions of all orders.