论文标题
随机单调性和马尔可夫产品
Stochastic monotonicity and the Markov product for copulas
论文作者
论文摘要
给定两个随机变量$ x $和$ y $，随机单调性描述了$ x $对$ y $的单调影响。我们证明，使用同构$ 2 $ populas和Markov操作员之间的同构符合$ 2 $ 2 $ - 流体的两种不同特征。第一种方法建立了随机单调的Copulas和具有单调性的Markov操作员之间的一对一对应关系。第二种方法是通过与马尔可夫产品相对于其单调性特性来随机性单调的表征。应用后一个结果，我们将所有自随机性单调copulas确定为独立copula $π$的序数总和。
Given two random variables $X$ and $Y$, stochastic monotonicity describes a monotone influence of $X$ on $Y$. We prove two different characterizations of stochastically monotone $2$-copulas using the isomorphism between $2$-copulas and Markov operators. The first approach establishes a one-to-one correspondence between stochastically monotone copulas and monotonicity-preserving Markov operators. The second approach characterizes stochastically monotone copulas by their monotonicity property with respect to the Markov product. Applying the latter result, we identify all idempotent stochastically monotone copulas as ordinal sums of the independence copula $Π$.
