Equivalent or absolutely continuous probability measures with given marginals
Patrizia Berti ; Luca Pratelli ; Pietro Rigo ; Fabio Spizzichino
Dependence Modeling, Tome 3 (2015), / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Let (X,A) and (Y,B) be measurable spaces. Supposewe are given a probability α on A, a probability β on B and a probability μ on the product σ-field A ⊗ B. Is there a probability ν on A⊗B, with marginals α and β, such that ν ≪ μ or ν ~ μ ? Such a ν, provided it exists, may be useful with regard to equivalent martingale measures and mass transportation. Various conditions for the existence of ν are provided, distinguishing ν ≪ μ from ν ~ μ.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:270847 
@article{bwmeta1.element.doi-10_1515_demo-2015-0004,
     author = {Patrizia Berti and Luca Pratelli and Pietro Rigo and Fabio Spizzichino},
     title = {Equivalent or absolutely continuous probability measures with given marginals},
     journal = {Dependence Modeling},
     volume = {3},
     year = {2015},
     zbl = {1328.60007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_demo-2015-0004}
}

Patrizia Berti; Luca Pratelli; Pietro Rigo; Fabio Spizzichino. Equivalent or absolutely continuous probability measures with given marginals. Dependence Modeling, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_demo-2015-0004/

[1] Berti, P., L. Pratelli, and P. Rigo (2014). A unifying view on some problems in probability and statistics. Stat. Methods Appl. 23(4), 483–500. [Crossref][WoS]

[2] Berti, P., L. Pratelli, and P. Rigo (2015). Two versions of the fundamental theorem of asset pricing. Electron. J. Probab. 20, 1–21. [WoS][Crossref] | Zbl 1326.60007

[3] Bhaskara Rao, K. P. S. and M. Bhaskara Rao (1983). Theory of Charges. Academic Press, New York. | Zbl 0516.28001

[4] Folland, G. B. (1984). Real Analysis: Modern Techniques and their Applications. Wiley, New York. | Zbl 0549.28001

[5] Korman, J. and R. J. McCann (2015). Optimal transportation with capacity constraints. Trans. Amer. Math. Soc. 367(3), 1501– 1521. | Zbl 1305.90065

[6] Ramachandran, D. (1979). Perfect Measures I and II. Macmillan, New Delhi. | Zbl 0523.60006

[7] Ramachandran, D. (1996). Themarginal problem in arbitrary product spaces. In Distributions with fixed marginals and related topics, 260–272. Inst. Math. Statist., Hayward.

[8] Strassen, V. (1965). The existence of probability measures with given marginals. Ann. Math. Statist 36, 423–439. [Crossref] | Zbl 0135.18701