High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs
High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs
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DOI：
10.1137/130935616
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发表时间：
2014-07
期刊：
影响因子：
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通讯作者：
A. Abdulle;G. Vilmart;K. Zygalakis
中科院分区：
文献类型：
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作者：
A. Abdulle;G. Vilmart;K. Zygalakis
本文引入了一种新的充分条件，使得一种数值方法能够以高阶精度逼近遍历随机微分方程系统的不变测度，而不依赖于该方法的弱阶精度。然后，我们提出了一个基于修正微分方程框架的系统程序，用于构造随机积分器，该积分器捕获了一类广泛的遍历SDEs（布朗动力学和朗之万动力学）的不变测度，其精度与底层方法的弱阶无关。数值实验证实了我们的理论发现。
We introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then present a systematic procedure based on the framework of modified differential equations for the construction of stochastic integrators that capture the invariant measure of a wide class of ergodic SDEs (Brownian and Langevin dynamics) with an accuracy independent of the weak order of the underlying method. Numerical experiments confirm our theoretical findings.