论文标题
关于强大的坠机特性，指数性的千古和大偏差原理，用于随机阻尼的汉密尔顿系统，其依赖状态依赖性开关
On Strong Feller Property, Exponential Ergodicity and Large Deviations Principle for Stochastic Damping Hamiltonian Systems with State-Dependent Switching
论文作者
论文摘要
这项工作着重于一类带有州依赖性切换的随机阻尼哈密顿系统，其中切换过程具有无限的状态空间。在非常温和的条件下通过Martingale方法确定了全球弱解决方案的存在和唯一性之后，该论文接下来证明了通过杀戮技术以及某些解决方案和过渡概率身份的杀戮技术来证明制度转换随机性抑制汉密尔顿系统的强大陷阱。在本文中，对切换率的常用连续性假设$ q_ {kl}（\ cdot）$放宽以衡量性。最后，本文提供了足够的条件，可以实现指数性的牙齿和大偏差原则，用于转换随机性抑制汉密尔顿系统。详细研究了有关制度开关范德尔和（过度抑制）Langevin系统的几个示例。
This work focuses on a class of stochastic damping Hamiltonian systems with state-dependent switching, where the switching process has a countably infinite state space. After establishing the existence and uniqueness of a global weak solution via the martingale approach under very mild conditions, the paper next proves the strong Feller property for regime-switching stochastic damping Hamiltonian systems by the killing technique together with some resolvent and transition probability identities. The commonly used continuity assumption for the switching rates $q_{kl}(\cdot)$ in the literature is relaxed to measurability in this paper. Finally the paper provides sufficient conditions for exponential ergodicity and large deviations principle for regime-switching stochastic damping Hamiltonian systems. Several examples on regime-switching van der Pol and (overdamped) Langevin systems are studied in detail for illustration.
