Optimal Non-reversible Linear Drift for the Convergence to Equilibrium of a Diffusion
Optimal Non-reversible Linear Drift for the Convergence to Equilibrium of a Diffusion
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DOI：
10.1007/s10955-013-0769-x
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发表时间：
2013-07-01
影响因子：
1.6
通讯作者：
Pavliotis, G. A.
中科院分区：
文献类型：
--
作者：
Lelievre, T.;Nier, F.;Pavliotis, G. A.
我们考虑不改变不变分布的可逆扩散的不可逆扰动，并问是否存在使收敛到平衡的速率最大化的最优扰动。我们通过证明这种最优摄动的存在性和提供一种易于实现的构造它们的算法来解决线性漂移情况下的这个问题。我们特别讨论了前因子在指数收敛估计中的作用。数值实验证明了我们严谨的结果。
We consider non-reversible perturbations of reversible diffusions that do not alter the invariant distribution and we ask whether there exists an optimal perturbation such that the rate of convergence to equilibrium is maximized. We solve this problem for the case of linear drift by proving the existence of such optimal perturbations and by providing an easily implementable algorithm for constructing them. We discuss in particular the role of the prefactor in the exponential convergence estimate. Our rigorous results are illustrated by numerical experiments.