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On ℝd-valued peacocks

Published online by Cambridge University Press:  21 May 2013

Francis Hirsch  and
Bernard Roynette
Francis Hirsch
Affiliation:
Laboratoire d’Analyse et Probabilités, Université d’Évry – Val d’Essonne, Boulevard F. Mitterrand, 91025 Évry Cedex, France. [email protected]
Bernard Roynette
Affiliation:
Institut Elie Cartan, Université Henri Poincaré, B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France; [email protected]
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Abstract

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].

Keywords

Convex ordermartingale1-martingalepeacock
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 444 - 454
Copyright
© EDP Sciences, SMAI, 2013

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References

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