对于高维概率分布，通常构造以这些分布为平稳分布的马氏过程对其进行估计. 本文主要考虑如何对这些分布更好地取样. 不同于实际应用中经常选择的可逆马氏过程，这里则是运用大偏差速率函数来分析和量化增加不可逆漂移后是如何提高取样效果的.

     本文分为三部分：第一部分介绍背景和主要结果；第二部分回顾了紧流形上可逆与不可逆扩散过程对目标分布的取样效果的比较，给出了一类特殊的不可逆扩散过程的模拟效果比较；第三部分考虑如何对欧氏空间上的目标分布进行更好地估计，讨论了可逆与不可逆，不同不可逆扩散过程的估计效果.

In order to sample from high dimensional probability distribution, we often
construct Markov process whose stationary distribution is the target distribution.
In this paper, we consider the question that how we can improve the sampling
properties. Instead of considering reversible Markov process, our main goal here is
using large deviation rate function to assess and quantify how the addition of a nonreversible part to original reversible process can be used to improve the sampling
properties.
The paper is divided into three parts. In the first part, we introduce the background and main results; in the second part, we recall the comparison of the sampling
properties of the reversible and irreversible diffusions in compact manifold, then we
give a comparison of the sampling properties of a special family of irreversible diffusions; in the third part, we consider how to sample better from a target distribution in Euclidean space, and compare the sampling properties between reversible and irreversible diffusions, and the sampling properties of different irreversible diffusions are also campared.