# On ℝd-valued peacocks

Francis Hirsch; Bernard Roynette

ESAIM: Probability and Statistics (2013)

- Volume: 17, page 444-454
- ISSN: 1292-8100

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topHirsch, Francis, and Roynette, Bernard. "On ℝd-valued peacocks." ESAIM: Probability and Statistics 17 (2013): 444-454. <http://eudml.org/doc/274361>.

@article{Hirsch2013,

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].},

author = {Hirsch, Francis, Roynette, Bernard},

journal = {ESAIM: Probability and Statistics},

keywords = {convex order; martingale; 1-martingale; peacock},

language = {eng},

pages = {444-454},

publisher = {EDP-Sciences},

title = {On ℝd-valued peacocks},

url = {http://eudml.org/doc/274361},

volume = {17},

year = {2013},

}

TY - JOUR

AU - Hirsch, Francis

AU - Roynette, Bernard

TI - On ℝd-valued peacocks

JO - ESAIM: Probability and Statistics

PY - 2013

PB - EDP-Sciences

VL - 17

SP - 444

EP - 454

AB - 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].

LA - eng

KW - convex order; martingale; 1-martingale; peacock

UR - http://eudml.org/doc/274361

ER -

## References

top- [1] P. Cartier, J.M.G. Fell and P.-A. Meyer, Comparaison des mesures portées par un convexe compact. Bull. Soc. Math. France92 (1964) 435–445. Zbl0154.39402MR206193
- [2] C. Dellacherie and P.-A. Meyer, Probabilités et potentiel, in Théorie des martingales, Chapitres V à VIII. Hermann (1980). Zbl0138.10402MR566768
- [3] J.L. Doob, Generalized sweeping-out and probability. J. Funct. Anal.2 (1968) 207–225. Zbl0186.50403MR222959
- [4] F. Hirsch and B. Roynette, A new proof of Kellerer’s theorem. ESAIM: PS 16 (2012) 48–60. Zbl1277.60041MR2911021
- [5] F. Hirsch, C. Profeta, B. Roynette and M. Yor, Peacocks and associated martingales, with explicit constructions. Bocconi & Springer Series 3 (2011). Zbl1227.60001MR2808243
- [6] H.G. Kellerer, Markov-Komposition und eine Anwendung auf Martingale. Math. Ann.198 (1972) 99–122. Zbl0229.60049MR356250
- [7] G. Lowther, Fitting martingales to given marginals. http://arxiv.org/abs/0808.2319v1 (2008).
- [8] V. Strassen, The existence of probability measures with given marginals. Ann. Math. Stat.36 (1965) 423–439. Zbl0135.18701MR177430

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