In this paper, coupling methods for diffusion processes are studied mainly to obtain upper bound estimates in two different probability metrics. We use the martingale approach and explore the construction of explicit coupling operators which are sometimes optimal. The paper presents some criteria for the success of coupling and for the finiteness of the moments of the coupling times. Rates of convergence in various metrics are also studied.
Mu-Fa Chen. Shao-Fu Li. "Coupling Methods for Multidimensional Diffusion Processes." Ann. Probab. 17 (1) 151 - 177, January, 1989. https://doi.org/10.1214/aop/1176991501