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• # Artykuł - szczegóły

2015 | 3 | 1 |

## Equivalent or absolutely continuous probability measures with given marginals

EN

### Abstrakty

EN
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.

EN

otrzymano
2015-02-21
zaakceptowano
2015-05-07
online
2015-05-25

### Twórcy

autor
• Dipartimento di Matematica Pura ed Applicata ”G. Vitali”, Universita’ di Modena e Reggio-Emilia, via Campi
213/B, 41100 Modena, Italy,
autor
• Accademia Navale, viale Italia 72, 57100 Livorno, Italy
autor
• Dipartimento di Matematica ”F. Casorati”, Universita’
di Pavia, via Ferrata 1, 27100 Pavia, Italy
autor
• Dipartimento di Matematica ”G. Castelnuovo”, Universita’ di Roma ”La Sapienza”, piazzale
A. Moro 5, 00185 Roma, Italy

### Bibliografia

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• [3] Bhaskara Rao, K. P. S. and M. Bhaskara Rao (1983). Theory of Charges. Academic Press, New York.
• [4] Folland, G. B. (1984). Real Analysis: Modern Techniques and their Applications. Wiley, New York.
• [5] Korman, J. and R. J. McCann (2015). Optimal transportation with capacity constraints. Trans. Amer. Math. Soc. 367(3), 1501– 1521.
• [6] Ramachandran, D. (1979). Perfect Measures I and II. Macmillan, New Delhi.
• [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]