耗散系统逼近的一种自适应格式
An adaptive scheme for the approximation of dissipative systems
摘要：
当漂移向量场不是全局Lipschitz时，我们提出了一种新的扩散方程的长时间近似方法。在这种假设下，正则显式欧拉格式--具有常数或递减步长--可能会爆炸，隐式欧拉格式是CPU时间昂贵的。我们引入的算法是显式的，我们证明了该方案的加权经验测度的任何弱极限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Hamilton耗散系统。
英文摘要：
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, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit Euler scheme 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.
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