In this paper, we study a method to sample from a target distribution $\pi$over $\mathbb{R}^d$ having a positive density with respect to the Lebesguemeasure, known up to a normalisation factor. This method is based on the Eulerdiscretization of the overdamped Langevin stochastic differential equationassociated with $\pi$. For both constant and decreasing step sizes in the Eulerdiscretization, we obtain non-asymptotic bounds for the convergence to thetarget distribution $\pi$ in total variation distance. A particular attentionis paid to the dependency on the dimension $d$, to demonstrate theapplicability of this method in the high dimensional setting. These boundsimprove and extend the results of (Dalalyan 2014).
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机译：在本文中，我们研究了一种从目标分布$ \ pi $超过$ \ mathbb {R} ^ d $的方法进行抽样的方法，该分布相对于Lebesguemeasure具有正密度，已知归一化因子。此方法基于与$ \ pi $关联的过阻尼的Langevin随机微分方程的Eulerdiscrett化。对于欧拉离散化中的恒定步长和递减步长，我们获得了非渐近边界，以收敛到总变化距离中的目标分布$ \ pi $。特别要注意对维数$ d $的依赖性，以证明该方法在高维环境中的适用性。这些界限可以改善并扩展（Dalalyan 2014）的结果。
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