We consider the Fokker-Planck equation with subcritical confinement force field which may not derive from a potential function. We prove the existence of a unique positive equilibrium of mass one and we establish some subgeometric, or geometric, rate of convergence to a multiple of this equilibrium (depending on the space to which belongs the initial datum) in many spaces. Our results generalize similar results introduced by Toscani, Villani [33] and Röckner, Wang [31] for some forces associated to a potential and extended by Douc, Fort, Guillin [12] and Bakry, Cattiaux, Guillin [4] for some general forces: however in our approach the spaces are more general, and the rates of convergence to equilibrium are sharper.

我们考虑具有亚临界约束力场的 Fokker-Planck 方程，该方程可能不是从势函数导出的。我们证明了质量为 1 的唯一正平衡的存在，并且我们在许多空间中建立了一些次几何或几何收敛到该平衡的倍数（取决于初始数据所属的空间）。我们的结果概括了 Toscani、Villani [33] 和 Röckner、Wang [31] 为一些与势相关的力引入的类似结果，并由 Douc、Fort、Guillin [12] 和 Bakry、Cattiaux、Guillin [4] 扩展为一些一般力：然而，在我们的方法中，空间更一般，收敛到平衡的速度更快。