论文标题
langevin $ \ boldsymbol { - } $ smoluchowski扩散的差异表征
A variational characterization of Langevin$\boldsymbol{-}$Smoluchowski diffusions
论文作者
论文摘要
我们表明，Langevin $ - $ Smoluchowski在路径空间上的测量在时间反转下是不变的，然后使用新颖的熵型标准对漂移进行随机控制。这些前向后的步骤重复应用导致一系列随机控制问题，其初始/末端分布会收敛到扩散的Gibbs概率度量，并且其值沿Langevin $ - $ -Smoluchowski流的相对熵沿相对于Gibbs度量降低至零。
We show that Langevin$-$Smoluchowski measure on path space is invariant under time-reversal, followed by stochastic control of the drift with a novel entropic-type criterion. Repeated application of these forward-backward steps leads to a sequence of stochastic control problems, whose initial/terminal distributions converge to the Gibbs probability measure of the diffusion, and whose values decrease to zero along the relative entropy of the Langevin$-$Smoluchowski flow with respect to this Gibbs measure.
