Research output: Contribution to journal › Article

Georgios Deligiannidis, Anthony Lee

Original language | English |
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Journal | The Annals of Applied Probability |

Accepted/In press | 27 Sep 2017 |

**Which ergodic averages have_Accepted27September2017_GREEN AAM**AAP1607_027R1A0_1_.pdf, 576 KB, application/pdf

Uploaded date:18 Jun 2018

Version:Accepted author manuscript

- https://www.e-publications.org/ims/submission/AAP/user/submissionFile/27556?confirm=8e406574
Accepted author manuscript

- https://arxiv.org/abs/1606.08373
Accepted author manuscript

We show that the class of L2 functions for which ergodic averages of a reversible Markov chain have finite asymptotic variance is determined by the class of L2 functions for which ergodic averages of its asso- ciated jump chain have finite asymptotic variance. This allows us to characterize completely which ergodic averages have finite asymptotic variance when the Markov chain is an independence sampler. From a practical perspective, the most important result identifies a simple suf- ficient condition for all ergodic averages of L2 functions of the primary variable in a pseudo-marginal Markov chain to have finite asymptotic variance.

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