随机小扰动下稳定流形的逼近

The Approximations of Stable Manifolds under Small Random Perturbations

研究随机小扰动下稳定流形的逼近.在一定条件下证明,当小参数ε→0+时,受加性噪声驱动的随机发展方程的稳定流形几乎处处收敛到确定系统的稳定流形.

The approximations of stable manifolds under small random perturbations are put under examination. It is proven that under certain conditions, as small parameter ε approximates zero, stable manifolds of the stochastic evolution equation driven by additive noise converge almost surely for sure to those of the deterministic system.