论文标题
关于多维单纯形的Diaconis和Freedman链的渐近行为
On the asymptotic behavior of the Diaconis and Freedman's chain in a multidimensional simplex
论文作者
论文摘要
在本文中，我们在多维单纯形中给出了Diaconis和Freedman链的设置，并考虑其渐近行为。通过在随机迭代函数理论和准紧凑型操作员理论中使用技术，我们首先提供了一些足够的条件，以确保不变概率度量的存在和唯一性。在某些特定情况下，我们给出了不变概率密度的明确公式。此外，我们将该链的所有行为完全分为二维。最终，讨论了该链的其他一些设置。
In this paper, we give out a setting of an Diaconis and Freedman's chain in a multidimensional simplex and consider its asymptotic behavior. By using techniques in random iterated functions theory and quasi-compact operators theory, we first give out some sufficient conditions which ensure the existence and uniqueness of an invariant probability measure. In some particular cases, we give out explicit formulas of the invariant probability density. Moreover, we completely classify all behaviors of this chain in dimensional two. Eventually, some other settings of the chain are discussed.
