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On h-Transforms of One-Dimensional Diffusions Stopped upon Hitting Zero

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Book cover In Memoriam Marc Yor - Séminaire de Probabilités XLVII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 2137))

Abstract

For a one-dimensional diffusion on an interval for which 0 is the regular-reflecting left boundary, three kinds of conditionings to avoid zero are studied. The limit processes are h-transforms of the process stopped upon hitting zero, where h’s are the ground state, the scale function, and the renormalized zero-resolvent. Several properties of the h-transforms are investigated.

In memoriam, Marc Yor

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Acknowledgements

The authors are thankful to Prof. Masatoshi Fukushima for drawing their attention to the paper [4]. They also thank Prof. Matsuyo Tomisaki and Dr. Christophe Profeta for their valuable comments.

The research of the first author, Kouji Yano, was supported by KAKENHI (26800058) and partially by KAKENHI (24540390). The research of the second author, Yuko Yano, was supported by KAKENHI (23740073).

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Authors and Affiliations

  1. Graduate School of Science, Kyoto University, Kyoto, Japan

    Kouji Yano

  2. Department of Mathematics, Kyoto Sangyo University, Kyoto, Japan

    Yuko Yano

Authors
  1. Kouji Yano
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  2. Yuko Yano
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Correspondence to Kouji Yano .

Editor information

Editors and Affiliations

  1. Laboratoire de Mathématiques, Université de Versailles-St Quentin, Versailles, France

    Catherine Donati-Martin

  2. Campus scientifique, IECL, Vandœuvre-lès-Nancy, France

    Antoine Lejay

  3. Laboratoire de Mathématiques, Université de Versailles-St Quentin, Versailles, France

    Alain Rouault

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Yano, K., Yano, Y. (2015). On h-Transforms of One-Dimensional Diffusions Stopped upon Hitting Zero. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) In Memoriam Marc Yor - Séminaire de Probabilités XLVII. Lecture Notes in Mathematics(), vol 2137. Springer, Cham. https://doi.org/10.1007/978-3-319-18585-9_7

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