Stochastic monotonicity and the Markov product for copulas

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:503

Article

Siburg, Karl Friedrich¹  Strothmann, Christopher¹ 

[1] TU Dortmund Univ, Fac Math, Dortmund, Germany

关键词: Stochastic monotonicity;    Copula;    Markov product;    Markov operator;   

DOI  :  10.1016/j.jmaa.2021.125348

来源: Elsevier

【 摘 要 】

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 Pi. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free