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A Sequence of Albin Type Continuous Martingales with Brownian Marginals and Scaling

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Séminaire de Probabilités XLIII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 2006))

Abstract

Closely inspired by Albin’s method which relies ultimately on the duplication formula for the Gamma function, we exploit Gauss’ multiplication formula to construct a sequence of continuous martingales with Brownian marginals and scaling.

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References

  1. Albin, J.M.P.: A continuous non-Brownian motion martingale with Brownian motion marginal distributions. Stat. Probab. Lett. 78(6), 682–686 (2008)

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  2. Andrews, G., Askey, R., Roy, R.: Special functions. Encyclopedia of Mathematics and its Applications, vol. 71. Cambridge University Press, Cambridge (1999)

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  3. Chaumont, L., Yor, M.: Exercises in probability. A guided tour from measure theory to random processes, via conditioning. Cambridge Series in Statistical and Probabilistic Mathematics, vol. 13. Cambridge University Press, Cambridge (2003)

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  4. Hamza, K., Klebaner, F.: A family of non-Gaussian martingales with Gaussian marginals. J. Appl. Math. Stoch. Anal. ID 92723, 19 pp. (2007)

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  5. Madan, D., Yor, M.: Making Markov martingales meet marginals: with explicit constructions. Bernoulli 8(4), 509–536 (2002)

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Authors and Affiliations

  1. Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie Université Paris 06 and CNRS, UMR 7599, 4, Place Jussieu, 75252, Paris Cedex 05, France

    David Baker, Catherine Donati-Martin & Marc Yor

  2. Institut Universitaire de France, Paris Cedex 05, France

    Marc Yor

Authors
  1. David Baker
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  2. Catherine Donati-Martin
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  3. Marc Yor
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Corresponding author

Correspondence to David Baker .

Editor information

Editors and Affiliations

  1. Lab. de Probabilités et Modèles Aléatoir, Université Pierre et Marie Curie, place Jussieu 4, Paris Cedex 05, 75252, France

    Catherine Donati-Martin

  2. IECN, Campus scientifique, BP 239, Nancy-Université, INRIA, Vandoeuvre-lès-Nancy, 54506, France

    Antoine Lejay

  3. Laboratoire de Mathématiques, Université de Versailles-St-Quentin, avenue des Etats-Unis 45, Versailles, 78035, France

    Alain Rouault

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Baker, D., Donati-Martin, C., Yor, M. (2011). A Sequence of Albin Type Continuous Martingales with Brownian Marginals and Scaling. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIII. Lecture Notes in Mathematics(), vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15217-7_20

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