论文标题
渐近稳定的马尔可夫半群的电子主管
The e-property of asymptotically stable Markov semigroups
论文作者
论文摘要
研究了渐近稳定性，最终的E-Property和Markov Semigroups的E-Property，并根据一般（波兰）度量空间定义的度量。虽然通常对渐近稳定性引起了很多关注（并且E-Property已被验证了多年以建立它），但应注意的是，E-Property本身也很重要，例如，确保模拟中的数值错误可忽略不计。 在这里，可以表明，任何具有不变措施的渐近马尔可夫人半群，以使其内部支持的内部是非空的，都可以满足最终的电子效果。此外，我们证明，任何马尔可夫 - 特莱尔半群（Markov-Feller Semigroup）具有很强的随机连续，并且具有最终的电子杂货，也具有电子杂志。我们还举办了一个示例，强调强烈的随机连续性不能被其弱的对应物所取代，除非与马尔可夫半群相对应的过程的状态空间是一个紧凑的公制空间。
The relations between asymptotic stability, the eventual e-property and the e-property of Markov semigroups, acting on measures defined on general (Polish) metric spaces, are studied. While usually much attention is paid to asymptotic stability (and the e-property has been for years verified only to establish it), it should be noted that the e-property itself is also important as it, e.g., ensures that numerical errors in simulations are negligible. Here, it is shown that any asymptotically stable Markov-Feller semigroup with an invariant measure such that the interior of its support is non-empty satisfies the eventual e-property. Moreover, we prove that any Markov-Feller semigroup, which is strongly stochastically continuous, and which possesses the eventual e-property, also has the e-property. We also present an example highlighting that strong stochastic continuity cannot be replaced by its weak counterpart, unless a state space of a process corresponding to a Markov semigroup is a compact metric space.
