论文标题
马尔可夫产品用于尾巴依赖功能
A Markov product for tail dependence functions
论文作者
论文摘要
我们引入了马尔可夫产品结构，用于基于著名的马尔可夫产品的多元尾部依赖功能。我们研究了该新产品的代数和单调性特性，以及它在描述Copulas Markov产品的尾巴行为中的作用。对于双变量情况，我们显示了其他平滑属性，并得出了同性体系的表征，以及n倍迭代的限制行为。最后，我们在双变量尾部依赖函数和一类阳性的定位算子之间建立一对一的对应关系。这些操作员都是$ l^1（\ mathbb {r} _+）$和$ l^\ infty（\ mathbb {r} _+）$上的收缩，并且构成了马尔可夫运营商的自然概括。
We introduce a Markov product structure for multivariate tail dependence functions, building upon the well-known Markov product for copulas. We investigate algebraic and monotonicity properties of this new product as well as its role in describing the tail behaviour of the Markov product of copulas. For the bivariate case, we show additional smoothing properties and derive a characterization of idempotents together with the limiting behaviour of n-fold iterations. Finally, we establish a one-to-one correspondence between bivariate tail dependence functions and a class of positive, substochastic operators. These operators are contractions both on $L^1(\mathbb{R}_+)$ and $L^\infty(\mathbb{R}_+)$ and constitute a natural generalization of Markov operators.
