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arXiv · 1610.02190

Weak decreasing stochastic order

Antoine-Marie Bogso·Patrice Takam Soh
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Abstract

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 Az\'ema-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.

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BibTeXRIS

Antoine-Marie Bogso, Patrice Takam Soh. 2016-10-07. Weak decreasing stochastic order. https://doi.org/10.1016/j.spl.2017.02.020

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