  In this article, we discuss subgeometric ergodicity of a class of
regime-switching diffusion processes. We derive conditions on the drift and
diffusion coefficients, and the switching mechanism which result in
subgeometric ergodicity of the corresponding semigroup with respect to the
total variation distance as well as a class of Wasserstein distances. At the
end, subgeometric ergodicity of certain classes of regime-switching Markov
processes with jumps is also discussed.
