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- By Theorem 15.0.1 of Meyn and Tweedie (2009) the process (at) is geometrically ergodic.
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- Proof. To show that the process (at) is geometrically ergodic, we use part (iii) of Theorem 15.0.1 of Meyn and Tweedie (2009). We need to verify that a the process {at+1}∞ t=0 is È−irreducible; b the process {at+1}∞ t=0 is aperiodic;15 and c there exists a petite set C,16 constants b < ∞, à> 0 and a function V ≥ 1 finite at some point in [y ,∞) satisfying EV (at+1) − V (at) ≤ −ÃÂV (at) + bIC(at), ∀at ∈ [y , ∞). By Lemma 6, the process {at+1}∞ t=0 is È−irreducible.
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