Advertisement

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

  • David Baker
  • Catherine Donati-Martin
  • Marc Yor
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, 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.

Martingales Brownian marginals 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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.
    Andrews, G., Askey, R., Roy, R.: Special functions. Encyclopedia of Mathematics and its Applications, vol. 71. Cambridge University Press, Cambridge (1999)Google Scholar
  3. 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)Google Scholar
  4. 4.
    Hamza, K., Klebaner, F.: A family of non-Gaussian martingales with Gaussian marginals. J. Appl. Math. Stoch. Anal. ID 92723, 19 pp. (2007)Google Scholar
  5. 5.
    Madan, D., 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

  • David Baker
    • 1
  • Catherine Donati-Martin
    • 1
  • Marc Yor
    • 1
    • 2
  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 FranceParis Cedex 05France

Personalised recommendations