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On Martingales with Given Marginals and the Scaling Property

  • David Baker
  • Marc Yor
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2006)

Abstract

In this short note, we draw the reader’s attention to a number of constructions of martingales with given marginals.

Martingales Brownian scaling Marginal distributions 

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References

  1. 1.
    Albin, J.M.P.: A continuous non-Brownian motion martingale with Brownian motion marginal distributions. Stat. Probab. Lett. 78(6), 682–686 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Baker, D., Donati-Martin, C., Yor, M.: Extending Albin’s construction of continuous martingales with Brownian marginals and scaling. Séminaire de Probabilités XLIII, in this volume, Lecture Notes in Math. Vol. 2006, Springer Verlag (2011)Google Scholar
  3. 3.
    Hirsch, F., Profeta, C., Roynette, B., Yor, M.: Constructing self-similar martingales via two Skorohod embeddings. Séminaire de Probabilités XLIII, in this volume, Lecture Notes in Math, Vol., 2006, Springer Verlag, (2011)Google Scholar
  4. 4.
    Hirsch, F., Profeta, C., Roynette, B., Yor, M.: Peacocks and associated martingales. Monograph in preparation (2010)Google Scholar
  5. 5.
    Kellerer, H.G.: Markov-Komposition und eine Anwendung auf Martingale. Math. Ann. 198(3), 99–122 (1972)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Lowther, G.: Fitting martingales to given marginals. Preprint arXiv:0808.2319 (2008)Google Scholar
  7. 7.
    Madan, D.B., Yor, M.: Making Markov martingales meet marginals: with explicit constructions. Bernoulli 8(4), 509–536 (2002)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Laboratoire de Probabilités et Modèles AléatoiresUniversité Pierre et Marie Curie, Université Paris 06, and CNRS, UMR 7599Paris Cedex 05France
  2. 2.Institut Universitaire de France and Laboratoire de Probabilités et Modèles AléatoiresUniversité Pierre et Marie Curie, Université Paris 06 and CNRS, UMR 7599Paris Cedex 05France

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