Let (Φt)t∈ℛ+ be a
Harris ergodic continuous-time Markov process on a general state space, with
invariant probability measure π. We investigate the rates of convergence of the transition function
Pt(x,·)
to π; specifically, we find conditions under which
r(t)|Pt(x,·)-π|→0 as t→∞,
for suitable subgeometric rate functions r(t), where |·| denotes the usual total variation
norm for a signed measure.
We derive sufficient conditions for the convergence to hold, in terms
of the existence of suitable points on which the first hitting time moments are bounded. In particular, for
stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These
results are illustrated in several examples.
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