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

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


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.


Brownian Motion Resolvent Operator Generalize Diffusion Natural Scale Bessel Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Graduate School of ScienceKyoto UniversityKyotoJapan
  2. 2.Department of MathematicsKyoto Sangyo UniversityKyotoJapan

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