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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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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