An adaptive scheme for the approximation of dissipative systems
An adaptive scheme for the approximation of dissipative systems
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耗散系统近似的自适应方案
DOI：
10.1016/j.spa.2007.02.004
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发表时间：
2005
影响因子：
1.4
通讯作者：
V. Lemaire
中科院分区：
文献类型：
--
作者：
V. Lemaire
本文提出了漂移矢量场非全局利普希茨时扩散的长时间逼近的一种新格式。在此假设下，常规的显式欧拉格式-具有恒定或递减步长-可能会爆炸，隐式欧拉格式是cpu时间昂贵的。所引入的算法是显式的，并证明了该格式的加权经验测度的任何弱极限都是随机微分方程的平稳分布。给出了几个例子，包括梯度耗散系统和哈密顿耗散系统。
We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, a regular explicit Euler scheme–with constant or decreasing step–may explode and implicit Euler schemes are CPU-time expensive. The algorithm we introduce is explicit and we prove that any weak limit of the weighted empirical measures of this scheme is a stationary distribution of the stochastic differential equation. Several examples are presented including gradient dissipative systems and Hamiltonian dissipative systems.