  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.
