Bounded conditional moments imply a geometric drift
= Bounded conditional moments imply a geometric drift
Suppose a <Markov kernel> satisfies $PV(x)\leq M<\infty$ for a measurable $V\geq1$. For $0<\rho<1$ and $R>M/\rho$, the sublevel set $C=\{V\leq R\}$ gives $PV\leq\rho V+M\mathbf1_C$. If $C$ is a <small set>, this is a <geometric drift condition>. The hypotheses of an <irreducible Markov chain> and an <aperiodic Markov chain> are also required for the usual <geometric ergodicity> theorem.