On ℝ d -valued peacocks
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 444-454

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].

DOI : 10.1051/ps/2012009
Classification : 60E15, 60G44, 60G15, 60G48
Keywords: convex order, martingale, 1-martingale, peacock 
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     title = {On $\mathbb {R}^d$-valued peacocks},
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Hirsch, Francis; Roynette, Bernard. On $\mathbb {R}^d$-valued peacocks. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 444-454. doi: 10.1051/ps/2012009

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