离散空间中 Fleming-Viot 粒子系统与准平稳分布的定量结果
概率论
2014-07-29 v2
摘要
对于一类离散 Fleming-Viot（或 Moran）型粒子系统，我们证明了在合适的 Wasserstein 耦合距离下，其收敛到平衡态是指数级的。该方法提供了收敛速率的显式定量估计。作为推论，我们证明了条件过程指数快速收敛到唯一的准平稳分布。此外，通过估计双粒子相关性，我们证明了 Fleming-Viot 过程一致地（关于时间）收敛到条件过程，并具有显式的收敛速率。我们在完全图和 N 个粒子在两点间跳跃的例子中说明了我们的结果。
引用
@article{arxiv.1312.2444,
title = {Quantitative results for the Fleming-Viot Particle system and quasi-stationary distributions in discrete space},
author = {Bertrand Cloez and Marie-Noémie Thai},
journal= {arXiv preprint arXiv:1312.2444},
year = {2014}
}
备注
New version of the paper "Quantitative results for the Fleming-Viot particle system in discrete space ". Some points are improved. For instance, Proof of chaos propagation is improved,, using Hardy's inequalities, we improve our results when the state space contains two points, the complete garph study is generalised, we add comments on our coupling construction