Solving the Poisson equation using coupled Markov chains
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908700468314112 |
|---|---|
| author | Douc, Randal Jacob, Pierre E. Lee, Anthony Vats, Dootika |
| author_facet | Douc, Randal Jacob, Pierre E. Lee, Anthony Vats, Dootika |
| contents | This article shows how coupled Markov chains that meet exactly after a random number of iterations can be used to generate unbiased estimators of the solutions of the Poisson equation. Through this connection, we re-derive known unbiased estimators of expectations with respect to the stationary distribution of a Markov chain and provide conditions for the finiteness of their moments. We further construct unbiased estimators of the asymptotic variance of Markov chain ergodic averages, and provide conditions for the finiteness of the estimators' moments of any order. If their second moment is finite, the average of independent copies of such estimators converges to the asymptotic variance at the Monte Carlo rate, comparing favorably to known rates for batch means and spectral variance estimators. The results are illustrated with numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_05691 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Solving the Poisson equation using coupled Markov chains Douc, Randal Jacob, Pierre E. Lee, Anthony Vats, Dootika Computation 65C40, 65C05, 60F05, 60J22, 60J05, 62F15 This article shows how coupled Markov chains that meet exactly after a random number of iterations can be used to generate unbiased estimators of the solutions of the Poisson equation. Through this connection, we re-derive known unbiased estimators of expectations with respect to the stationary distribution of a Markov chain and provide conditions for the finiteness of their moments. We further construct unbiased estimators of the asymptotic variance of Markov chain ergodic averages, and provide conditions for the finiteness of the estimators' moments of any order. If their second moment is finite, the average of independent copies of such estimators converges to the asymptotic variance at the Monte Carlo rate, comparing favorably to known rates for batch means and spectral variance estimators. The results are illustrated with numerical experiments. |
| title | Solving the Poisson equation using coupled Markov chains |
| topic | Computation 65C40, 65C05, 60F05, 60J22, 60J05, 62F15 |
| url | https://arxiv.org/abs/2206.05691 |