论文标题
在歧管上取样千古的随机微分方程的不变度度量的顺序条件
Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds
论文作者
论文摘要
我们得出了一种用于构建高级积分器的新方法，用于对具有歧视的动力学的动力学来采样千古随机微分方程的不变度量。我们获得了对应用于受约束过度抑制的langevin方程的一类runge-kutta方法进行不变度度量的顺序条件。该分析对于任意高阶有效，并依赖于外来芳香屠夫系列形式的扩展。为了说明方法，引入了第二阶方法，并在球体，圆环和特殊线性组上进行数值实验证实了理论发现。
We derive a new methodology for the construction of high order integrators for sampling the invariant measure of ergodic stochastic differential equations with dynamics constrained on a manifold. We obtain the order conditions for sampling the invariant measure for a class of Runge-Kutta methods applied to the constrained overdamped Langevin equation. The analysis is valid for arbitrarily high order and relies on an extension of the exotic aromatic Butcher-series formalism. To illustrate the methodology, a method of order two is introduced, and numerical experiments on the sphere, the torus and the special linear group confirm the theoretical findings.
