Volume 17, 2013
|Page(s)||444 - 454|
|Published online||21 May 2013|
On ℝd-valued peacocks
Laboratoire d’Analyse et Probabilités, Université d’Évry – Val
d’Essonne, Boulevard F.
2 Institut Elie Cartan, Université Henri Poincaré, B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France
Received: 26 July 2011
Revised: 17 April 2012
In this paper, we consider ℝd-valued integrable processes which are increasing in the convex order, i.e. ℝd-valued peacocks in our terminology. After the presentation of some examples, we show that an ℝd-valued process is a peacock if and only if it has the same one-dimensional marginals as an ℝd-valued martingale. This extends former results, obtained notably by Strassen [Ann. Math. Stat. 36 (1965) 423–439], Doob [J. Funct. Anal. 2 (1968) 207–225] and Kellerer [Math. Ann. 198 (1972) 99–122].
Mathematics Subject Classification: 60E15 / 60G44 / 60G15 / 60G48
Key words: Convex order / martingale / 1-martingale / peacock
© EDP Sciences, SMAI, 2013
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