On Stein's method for stochastically monotone single-birth chains
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916471306715136 |
|---|---|
| author | Daly, Fraser |
| author_facet | Daly, Fraser |
| contents | We discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's equation for such a process. Applications include rates of convergence to stationarity, and bounding the total variation distance between the stationary distributions of two Markov chains in the case where one transition matrix dominates the other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_00376 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Stein's method for stochastically monotone single-birth chains Daly, Fraser Probability 60J10 (Primary) 60E15, 60F05, 62E17 (Secondary) We discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's equation for such a process. Applications include rates of convergence to stationarity, and bounding the total variation distance between the stationary distributions of two Markov chains in the case where one transition matrix dominates the other. |
| title | On Stein's method for stochastically monotone single-birth chains |
| topic | Probability 60J10 (Primary) 60E15, 60F05, 62E17 (Secondary) |
| url | https://arxiv.org/abs/2207.00376 |