论文标题
中心弗莱明·维奥特（Fleming-Viot）过程的存在，唯一性和奇迹性
Existence, uniqueness and ergodicity for the centered Fleming-Viot process
论文作者
论文摘要
由偏见不变的fleming-viot过程的问题激励，我们考虑了居中的fleming-viot过程$ \ left（z_ {t} \ right）_ {t \ geqslant 0} $由$ z_ {t}定义的，t \ z_ {t} \ right \ rangle} \ sharp \，y_ {t} $，其中$ \ left（y_ {t} \ right）_ {t \ geqslant 0} $是原始的fleming-viot过程。我们的目标是通过Martingale问题来表征以弗莱明·维奥特（Fleming-Viot）为中心的过程。为了确定解决这个婚姻问题的解决方案，我们利用了原始的Fleming-Viot Martingale问题和渐近扩张。唯一性的证明是基于二元方法的弱版本，使我们能够在最初的条件下证明具有有限矩的独特性。我们还提供了反示例，表明我们基于二元性方法的方法不能期望为更一般的初始条件提供独特性。最后，我们在中心的Fleming-Viot过程中建立了具有指数收敛性的真实性特性，并表征了不变度的度量。
Motivated by questions of ergodicity for shift invariant Fleming-Viot process, we consider the centered Fleming-Viot process $\left(Z_{t} \right)_{t\geqslant 0}$ defined by $Z_{t} := τ_{-\left\langle {\rm id}, Y_{t} \right\rangle} \sharp \, Y_{t}$, where $\left(Y_{t}\right)_{t\geqslant 0}$ is the original Fleming-Viot process. Our goal is to characterise the centered Fleming-Viot process with a martingale problem. To establish the existence of a solution to this martingale problem, we exploit the original Fleming-Viot martingale problem and asymptotic expansions. The proof of uniqueness is based on a weakened version of the duality method, allowing us to prove uniqueness for initial conditions admitting finite moments. We also provide counter examples showing that our approach based on the duality method cannot be expected to give uniqueness for more general initial conditions. Finally, we establish ergodicity properties with exponential convergence in total variation for the centered Fleming-Viot process and characterise the invariant measure.
