Weak backward error analysis for overdamped Langevin processes
Weak backward error analysis for overdamped Langevin processes
复制标题
DOI：
10.1093/imanum/dru016
复制
发表时间：
2013-10
期刊：
影响因子：
--
通讯作者：
M. Kopec
中科院分区：
文献类型：
--
作者：
M. Kopec
考虑过阻尼Langevin随机微分方程的隐式数值逼近。我们示出了一个弱向后误差分析结果的意义上，与数值解相关联的生成器与修改后的Kolmogorov方程的解决方案相一致的高阶项的步长。这意味着数值格式的每一个测度都接近于由渐近展开得到的修正不变测度。此外，我们证明，可忽略不计的条款，与所考虑的隐式计划的动态是指数混合。
We consider numerical approximations of overdamped Langevin stochastic differential equations by implicit methods. We show a weak backward error analysis result in the sense that the generator associated with the numerical solution coincides with the solution of a modified Kolmogorov equation up to high order terms with respect to the stepsize. This implies that every measure of the numerical scheme is close to a modified invariant measure obtained by asymptotic expansion. Moreover, we prove that, up to negligible terms, the dynamic associated with the implicit scheme considered is exponentially mixing.