| Issue |
ESAIM: PS
Volume 17, 2013
|
|
|---|---|---|
| Page(s) | 444 - 454 | |
| DOI | https://doi.org/10.1051/ps/2012009 | |
| Published online | 21 May 2013 | |
On ℝd-valued peacocks
1
Laboratoire d’Analyse et Probabilités, Université d’Évry – Val
d’Essonne, Boulevard F.
Mitterrand, 91025
Évry Cedex,
France
francis.hirsch@univ-evry.fr
2
Institut Elie Cartan, Université Henri Poincaré,
B.P. 239, 54506
Vandœuvre-lès-Nancy Cedex,
France
bernard.roynette@iecn.u-nancy.fr
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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