论文标题
随机动力学系统的条件lyapunov频谱
The conditioned Lyapunov spectrum for random dynamical systems
论文作者
论文摘要
我们确定了具有吸收的无内存随机动力学系统的Lyapunov指数的全谱。为此，我们至关重要地嵌入了从未被吸收的过程，即$ q $ - 过程中，将其嵌入随机动力学系统的框架中，从而使我们能够研究乘法性细胞性能。我们表明，有限的lyapunov指数在条件概率中收敛，并将结果应用于迭代功能系统和随机微分方程。
We establish the existence of a full spectrum of Lyapunov exponents for memoryless random dynamical systems with absorption. To this end, we crucially embed the process conditioned to never being absorbed, the $Q$-process, into the framework of random dynamical systems, allowing us to study multiplicative ergodic properties. We show that the finite-time Lyapunov exponents converge in conditioned probability and apply our results to iterated function systems and stochastic differential equations.
