Kyoto Journal of Mathematics

Diffusions with Bessel-like drifts

Yuji Kasahara and Shin’ichi Kotani

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Linear diffusions which are not far from Bessel diffusions are considered. Specifically, the regular variation of Feller’s canonical measure is interpreted in terms of the drift coefficient. As an application, the asymptotic behavior of the transition probability at large times is discussed.

Article information

Kyoto J. Math., Volume 55, Number 4 (2015), 773-797.

Received: 21 November 2013
Revised: 4 September 2014
Accepted: 16 September 2014
First available in Project Euclid: 25 November 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 34B24: Sturm-Liouville theory [See also 34Lxx]

Spectral measure diffusion transition density Tauberian theorem


Kasahara, Yuji; Kotani, Shin’ichi. Diffusions with Bessel-like drifts. Kyoto J. Math. 55 (2015), no. 4, 773--797. doi:10.1215/21562261-3157739.

Export citation


  • [1] N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation, Encyclopedia Math. Appl. 27, Cambridge Univ. Press, Cambridge, 1987.
  • [2] A. N. Borodin and P. Salminen, Handbook of Brownian Motion—Facts and Formulae, 2nd ed., Birkhäuser, Basel, 2002.
  • [3] J. M. Harrison and L. A. Shepp, On skew Brownian motion, Ann. Probab. 9 (1981), 309–313.
  • [4] K. Itô, Essentials of Stochastic Processes, Transl. Math. Monogr. 231, Amer. Math. Soc., Providence, 2006.
  • [5] K. Itô and H. P. McKean, Jr., Diffusion Processes and Their Sample Paths, Grundlehren Math. Wiss. 125, Springer, New York, 1974.
  • [6] J. Karamata, Sur un mode de croissance régulière. Théorèmes fondamentaux, Bull. Soc. Math. France 61 (1953), 55–62.
  • [7] Y. Kasahara, Spectral theory of generalized second order differential operators and its applications to Markov processes, Japan. J. Math. (N.S.) 1 (1975/76), 67–84.
  • [8] Y. Kasahara, Spectral function of Krein’s and Kotani’s string in the class $\Gamma$, Proc. Japan Acad. Ser. A Math. Sci. 88 (2012), 173–177.
  • [9] Y. Kasahara and S. Watanabe, Asymptotic behavior of spectral measures of Krein’s and Kotani’s strings, Kyoto J. Math. 50 (2010), 623–644.
  • [10] S. Kotani, Krein’s strings with singular left boundary, Rep. Math. Phys. 59 (2007), 305–316.
  • [11] S. Kotani, Krein’s strings whose spectral functions are of polynomial growth, Kyoto J. Math. 53 (2013), 787–814.
  • [12] M. Tomisaki and M. Yamazato, Limit theorems for hitting times of 1-dimensional generalized diffusions, Nagoya Math. J. 152 (1998), 1–37.
  • [13] S. Watanabe, “Generalized arc-sine laws for one-dimensional diffusion processes and random walks” in Stochastic Analysis (Ithaca, NY, 1993), Proc. Sympos. Pure Math. 57, Amer. Math. Soc., Providence, 1995, 157–172.
  • [14] Y. Yano, On the occupation time on the half line of pinned diffusion processes, Publ. Res. Inst. Math. Sci. 42 (2006), 787–802.