Search

Based on the theory of M -matrix and Perron–Frobenius theorem, we provide some criteria to justify the convergence of the regime-switching diffusion processes in Wasserstein distances. The cost function we used to define the Wasserstein distance is not necessarily bounded. The continuous time Markov chains with finite and infinite countable state space are all studied. To deal with the infinite countable state space, we put forward a finite partition method. The boundedness for state-dependent regime-switching diffusions in an infinite countable state space is also studied. [ABSTRACT FROM AUTHOR]

In this paper we obtain based on an idea of M. Knott and C. S. Smith (1994, Linear Algebra Appl.199, 363–371) characterizations of solutions of three-coupling problems by reduction to the construction of optimal couplings of each of the variables to the sum. In the case of normal distributions this leads to a complete solution. Under a technical condition this idea also works for general distributions and one obtains explicit results. We extend these results to the n-coupling problem and derive a characterization of optimal n-couplings by several 2-coupling problems. This leads to some constructive existence results for Monge solutions. [Copyright &y& Elsevier]