Fokker-Planck 方程下 Rényi 散度的指数衰减
偏微分方程分析
2019-06-19 v2
摘要
我们证明了由严格凸势的梯度给出漂移项的 Fokker-Planck 方程之解向平衡态的指数收敛性, 并以 Rényi 散度量化。这推广了关于同一方程相对熵的经典指数衰减结果。
引用
@article{arxiv.1805.06554,
title = {Exponential decay of R\'enyi divergence under Fokker-Planck equations},
author = {Yu Cao and Jianfeng Lu and Yulong Lu},
journal= {arXiv preprint arXiv:1805.06554},
year = {2019}
}
备注
Exponential convergence rate in Theorem 1.2 has been improved and a simpler proof is provided