关于多维单形中Diaconis链和Freedman链的渐近性
On the asymptotic behavior of the Diaconis and Freedman's chain in a multidimensional simplex
摘要：
本文给出了多维单形中Diaconis-Freedman链的一个设定，并讨论了它的渐近性态。利用随机迭代函数理论和拟紧算子理论中的技巧，首先给出了保证不变概率测度存在唯一的若干充分条件。在某些特殊情况下，给出了不变概率密度的显式表达式。此外，我们完全分类的所有行为，这个链在二维。最后，讨论了链的其他设置。
英文摘要：
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.
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