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On conditioning random walks in an exponential family to stay nonnegative

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Book cover Séminaire de Probabilités XXVIII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1583))

Abstract

We show that the probability measures resulting from conditioning different random walks in an exponential family to stay nonnegative coincide with the measures obtained by taking one member of the family and conditioning it both to stay nonnegative and to go to infinity at a prescribed rate. This extends results in [1] where this relation was established for certain special members of an exponential family.

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References

  1. Bertoin, J. and Doney, R.A.: On conditioning a random walk to stay nonnegative, Ann. Probab. (to appear).

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Author information

Authors and Affiliations

  1. Laboratoire de Probabilités (CNRS), Université Paris VI, 4 Place Jussieu, 75252, Paris Cedex 05, France

    J. Bertoin

  2. Statistical Laboratory, Department of Mathematics, University of Manchester, M13 9PL, UK

    R. A. Doney

Authors
  1. J. Bertoin
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  2. R. A. Doney
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Editor information

Jacques Azéma Marc Yor Paul André Meyer

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© 1994 Springer-Verlag

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Bertoin, J., Doney, R.A. (1994). On conditioning random walks in an exponential family to stay nonnegative. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXVIII. Lecture Notes in Mathematics, vol 1583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073840

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  • DOI: https://doi.org/10.1007/BFb0073840

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58331-8

  • Online ISBN: 978-3-540-48656-5

  • eBook Packages: Springer Book Archive

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