论文标题
小lévy扰动下的哈密顿系统的Lyapunov指数
Lyapunov Exponents for Hamiltonian Systems under Small Lévy Perturbations
论文作者
论文摘要
这项工作是为了调查（顶部）Lyapunov指数，用于在小型非高斯Lévy噪声下的一类哈密顿系统。在合适的移动框架中，这种系统的线性化可以视为尼尔疗法线性系统的小扰动。然后，在适当的假设下，通过对平滑度，千古和集成性的假设来估算Lyapunov指数估计并应用Khas'minskii公式。最后，存在两个例子来说明我们的结果。结果表征了在哈密顿结构与非高斯不确定性之间相互作用下的一类动力系统的增长或衰减速率。
This work is to investigate the (top) Lyapunov exponent for a class of Hamiltonian systems under small non-Gaussian Lévy noise. In a suitable moving frame, the linearisation of such a system can be regarded as a small perturbation of a nilpotent linear system. The Lyapunov exponent is then estimated by taking a Pinsky-Wihstutz transformation and applying the Khas'minskii formula, under appropriate assumptions on smoothness, ergodicity and integrability. Finally, two examples are present to illustrate our results. The results characterize the growth or decay rates of a class of dynamical systems under the interaction between Hamiltonian structures and non-Gaussian uncertainties.
