We provide explicit expressions for the constants involved in the
characterisation of ergodicity of sub-geometric Markov chains. The constants
are determined in terms of those appearing in the assumed drift and one-step
minorisation conditions. The result is fundamental for the study of some
algorithms where uniform bounds for these constants are needed for a family of
Markov kernels. Our result accommodates also some classes of inhomogeneous
chains.Comment: 14 page
