Moderate deviations for the Langevin equations: Strong damping and fast Markovian switching
Moderate deviations for the Langevin equations: Strong damping and fast Markovian switching
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DOI：
10.1063/5.0095042
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发表时间：
2022-12
影响因子：
1.3
通讯作者：
Hongjiang Qian;G. Yin
中科院分区：
文献类型：
--
作者：
Hongjiang Qian;G. Yin
本文给出了一类具有强阻尼和快速马尔可夫切换的Langevin动力系统的中偏差原理。为了便于我们的研究，首先，分析系统的有界漂移处理。为了得到期望的适度偏差，证明了朗之万方程解的指数紧性。然后，它的一阶近似使用本地MDP的解决方案进行检查。最后，建立MDPs。为了使无界漂移的治疗，减少技术的文件，这表明，Lipschitz连续漂移可以处理。
In this paper, we obtain a moderate deviations principle (MDP) for a class of Langevin dynamic systems with a strong damping and fast Markovian switching. To facilitate our study, first, analysis of systems with bounded drifts is dealt with. To obtain the desired moderate deviations, the exponential tightness of the solution of the Langevin equation is proved. Then, the solution of its first-order approximation using local MDPs is examined. Finally, the MDPs are established. To enable the treatment of unbounded drifts, a reduction technique is presented near the end of the paper, which shows that Lipschitz continuous drifts can be dealt with.