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Some remarks on Pitman’s theorem

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Séminaire de Probabilités XXXI

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1655))

Abstract

Pitman constructs BES3 (0) as 2M−X where X is BM1 (0) and M t =supr≤t X r . Equivalently, X−2J is BM1 (0) when X is BES3 (0) and J t =infr≥t X r . Now the fact that X−2J gives a local martingale may be extended to a general result, for linear diffusions. In particular, if X is a linear diffusion, we introduce a general class of nontrivial transformations ϕ such that Z=ϕ(X, J) is a local martingale.

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Authors and Affiliations

  1. NWF I-Mathematik, Universität Regensburg, D-93040, Regensburg, Germany

    Bernhard Rauscher

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  1. Bernhard Rauscher
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Jacques Azéma Marc Yor Michel Emery

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© 1997 Springer-Verlag Berlin Heidelberg

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Rauscher, B. (1997). Some remarks on Pitman’s theorem. In: Azéma, J., Yor, M., Emery, M. (eds) Séminaire de Probabilités XXXI. Lecture Notes in Mathematics, vol 1655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0119312

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  • DOI: https://doi.org/10.1007/BFb0119312

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62634-3

  • Online ISBN: 978-3-540-68352-0

  • eBook Packages: Springer Book Archive

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