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 order, martingale, 1-martingale, peacock
@article{PS_2013__17__444_0, author = {Hirsch, Francis and Roynette, Bernard}, title = {On $\mathbb {R}^d$-valued peacocks}, journal = {ESAIM: Probability and Statistics}, pages = {444--454}, publisher = {EDP-Sciences}, volume = {17}, year = {2013}, doi = {10.1051/ps/2012009}, zbl = {1291.60085}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps/2012009/} }
TY - JOUR AU - Hirsch, Francis AU - Roynette, Bernard TI - On $\mathbb {R}^d$-valued peacocks JO - ESAIM: Probability and Statistics PY - 2013 SP - 444 EP - 454 VL - 17 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2012009/ DO - 10.1051/ps/2012009 LA - en ID - PS_2013__17__444_0 ER -
Hirsch, Francis; Roynette, Bernard. On $\mathbb {R}^d$-valued peacocks. ESAIM: Probability and Statistics, Volume 17 (2013), pp. 444-454. doi : 10.1051/ps/2012009. http://archive.numdam.org/articles/10.1051/ps/2012009/
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