Weak decreasing stochastic order

Bogso, AM; Soh, PT

Bogso, AM (reprint author), Univ Yaounde I, Dept Math, POB 812, Yaounde, Cameroon.

STATISTICS & PROBABILITY LETTERS, 2017; 126 ( ): 49

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 family of integrable probability measures with negative mean to be embeddable in a standard Brownian motion by the Cox and Hobson extension of the Azema-Yor algorithm. The resulting process is a supermartingale and if, in addition, the measures have densities, this supermartingale is Markovian. Then the Cox Hobson algorithm provides a special solution of Kellerer's theorem relying on the stronger hypothesis of WDS order. (C) 2017 Elsevier B.V. All rights reserved.

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