Lyapunov Exponents of Nonlinear Stochastic Differential Equations with Jumps
Lyapunov Exponents of Nonlinear Stochastic Differential Equations with Jumps
复制标题
带跳跃的非线性随机微分方程的李亚普诺夫指数
DOI：
10.1007/978-3-0348-8069-5_19
复制
发表时间：
2003
影响因子：
6.8
通讯作者：
C. W. Li
中科院分区：
文献类型：
--
作者：
C. W. Li
对于一类具有跳变的非线性随机微分方程，存在一个不变的概率测度µ。Lyapunov指数qµ可以用Furstenberg-Has 'minskii公式表示为对遍历不变测度的积分，因此几乎确定的渐近稳定性依赖于qµ的符号。如果相应的扩散是非简并的，则µ是唯一的，并且在C（∈d）中具有严格正不变密度。
For a certain kind of nonlinear stochastic differential equations with jumps in ℝ d , there exists an invariant probability measure µ on ℝ d . A Lyapunov exponent q µ can be represented by the Furstenberg—Has’minskii formula as an integral over ℝ d with respect to the ergodic invariant measure, so that the almost sure asymptotic stability depends on the sign of q µ . If the corresponding diffusion is nondegenerate, then µ is unique and has strictly positive invariant density in C(ℝ d ).