This work is devoted to a class of Langevin equations involving strong damping and fast Markov switching. Modeling using continuous dynamics and discrete events together with their interactions much enlarged the applicability of Langevin equations in a random environment. Strong damping and fast switching are characterized by the use of multiple small parameters, resulting in singularly perturbed systems. The motivation of our work stems from the reduction of complexity for complex systems. Under suitable conditions, it is established that the solutions of the Langevin equations satisfy a large deviations principle. Then, we apply our results to statistical physics problems of a small particle in time-inhomogeneous environment and low temperature. Some connections to other fields in physics are also given.

中文翻译：

---

一类具有强阻尼和快速切换的马尔可夫切换朗之万方程

这项工作致力于一类涉及强阻尼和快速马尔可夫切换的朗之万方程。使用连续动力学和离散事件及其相互作用进行建模大大扩大了朗之万方程在随机环境中的适用性。强阻尼和快速切换的特点是使用多个小参数，导致系统受到奇异扰动。我们工作的动机源于复杂系统复杂性的降低。在合适的条件下，建立了朗之万方程的解满足大偏差原理。然后，我们将我们的结果应用于时间不均匀环境和低温下小粒子的统计物理问题。还给出了与物理学其他领域的一些联系。