论文标题
$ \ mathbb r^d $的扩散几乎确定收缩。应用于广义的Langevin扩散
Almost sure contraction for diffusions on $\mathbb R^d$. Application to generalised Langevin diffusions
论文作者
论文摘要
对于$ \ Mathbb r^d $具有恒定扩散矩阵的扩散，而不假设可逆性或低纤维化性，我们证明确定性漂移的合同性等于wasserstein距离$ \ \ \ \ \ \ \ m natercal w_p w_p $，$ p \ in [1，$ p \ in [1，\ infty] $。这也意味着该过程的厄运手段的集中不平等。然后，当势振荡器的某些非平衡链和一些广义的兰格文鸟扩散时，建立了这种合同性能，当电势是有界的黑森州凸出的，并且摩擦足够高。这扩展了常规（动力学）兰格文扩散的先前已知结果。
In the case of diffusions on $\mathbb R^d$ with constant diffusion matrix, without assuming reversibility nor hypoellipticity, we prove that the contractivity of the deterministic drift is equivalent to the constant rate contraction of Wasserstein distances $\mathcal W_p$, $p\in[1,\infty]$. It also implies concentration inequalities for ergodic means of the process. Such a contractivity property is then established for some non-equilibrium chains of anharmonic oscillators and for some generalised Langevin diffusions when the potential is convex with bounded Hessian and the friction is sufficiently high. This extends previous known results for the usual (kinetic) Langevin diffusion.
