Convergence rate to the stationary distribution for continuous-time Markov processes can be studied using Lyapunov functions. Recent work by the author provided explicit rates of convergence in special case of a reflected jump-diffusion on a half-line. These results are proved for total variation distance and its generalizations: measure distances defined by test functions regardless of their continuity. Here we prove similar results for Wasserstein distance, convergence in which is related to convergence for continuou test functions. In some cases, including the reflected Ornstein-Uhlenbeck process, we get faster exponential convergence rates for Wasserstein distance than for total variation distance.

中文翻译：

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反射跳跃扩散的 Wasserstein 距离平衡收敛率

可以使用李雅普诺夫函数研究连续时间马尔可夫过程的平稳分布的收敛率。作者最近的工作在半线上反射跳跃扩散的特殊情况下提供了明确的收敛率。这些结果证明了总变异距离及其泛化：测量由测试函数定义的距离，而不管它们的连续性。在这里，我们证明了 Wasserstein 距离的类似结果，收敛性与连续测试函数的收敛性有关。在某些情况下，包括反射的 Ornstein-Uhlenbeck 过程，与总变异距离相比，Wasserstein 距离的指数收敛速度更快。