论文标题
Dawson-Watanabe类型流程的奇迹和指数成分
Ergodicities and exponential ergodicities of Dawson-Watanabe type processes
论文作者
论文摘要
在自然的假设下，我们证明了瓦斯坦斯坦（Wasserstein）和道森（Watanabe Superprocesses）的瓦斯坦（Wasserstein）的奇异性和指数成分距离，而没有移民或移民。 The strong Feller property in the total variation distance is derived as a by-product.该方法的关键是对过渡概率变化的一组估计值。 Wasserstein距离的估计值源自超级过程的第一瞬间引起的内核的上限。总变化距离的那些基于对超级过程的累积半群与连续态分支过程的比较。结果大大改善并扩展了Stannat（2003a，2003b）和Friesen（2019+）的结果。我们还展示了相关的移民超级过程和可分解分布之间的长期性之间的联系。
Under natural assumptions, we prove the ergodicities and exponential ergodicities in Wasserstein and total variation distances of Dawson--Watanabe superprocesses without or with immigration. The strong Feller property in the total variation distance is derived as a by-product. The key of the approach is a set of estimates for the variations of the transition probabilities. The estimates in Wasserstein distance are derived from an upper bound of the kernels induced by the first moment of the superprocess. Those in total variation distance are based on a comparison of the cumulant semigroup of the superprocess with that of a continuous-state branching process. The results improve and extend considerably those of Stannat (2003a, 2003b) and Friesen (2019+). We also show a connection between the ergodicities of the associated immigration superprocesses and decomposable distributions.
