Publications scientifiques
2016PrépublicationanglaisAccès ouvert
Weak decreasing stochastic order (ouvre dans un nouvel onglet)
Auteurs
Université de Yaoundé I
Antoine-Marie Bogso
arXiv (Cornell University)
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Publications scientifiques
Antoine-Marie Bogso
arXiv (Cornell University)
We introduce the notion of weak decreasing stochastic (WDS) ordering for real-valued processes with negative means, which, to our knowledge, has not been studied before. Thanks to Madan-Yor's argument, it follows that the WDS ordering is a necessary and sufficient condition for a process with negative mean to be embeddable in a standard Brownian motion by the Cox and Hobson extension of the Azéma-Yor algorithm. Since the decreasing stochastic order is stronger than the WDS order, then, for every stochastically non-decreasing family of probability measures with densities, the Cox-Hobson stopping times provide an associated Markov process. The quantile process associated to a stochastically non-decreasing process is not necessarily Markovian.