A stronger property is geometric ergodicity. For any signed measure
on 
, let 
denote the total variation of .
A Markov chain is geometrically ergodic if there exists a
constant r ;SPMgt; 1 such that
This is implied (Meyn and Tweedie, 1993, Theorem 15.0.1) by the
geometric drift condition: there exists a function
, constants 
and 
,
and a small set 
such that
Any V that satisfies the geometric drift condition is unbounded off small sets (when the chain is aperiodic). Hence the geometric drift condition implies the drift condition for recurrence.
It should be noted that neither of these proofs has any novelty. They follow exactly the logic of the proofs for the Strauss process sampler given in Geyer and Møller (1994). The only point of repeating them here is to show that the same argument works for any point process with unnormalized density having bounded conditional intensity.
