Journal of Mathematics of Kyoto University

A density formula for the law of time spent on the positive side of one-dimensional diffusion processes

Shinzo Watanabe, Kouji Yano, and Yuko Yano

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Abstract

We show the existence and continuity of the density and obtain its formula for the law of the fraction of time spent on the positive side of a very general class of one-dimensional (generalized or gap) diffusion processes. We also study the asymptotic properties of the density at the extreme values $x = 0$ and $x = 1$, which extend, in particular, some recent results by Kasahara and Yano [8].

Article information

Source
J. Math. Kyoto Univ., Volume 45, Number 4 (2005), 781-806.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250281657

Digital Object Identifier
doi:10.1215/kjm/1250281657

Mathematical Reviews number (MathSciNet)
MR2226630

Zentralblatt MATH identifier
1102.60068

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]

Citation

Watanabe, Shinzo; Yano, Kouji; Yano, Yuko. A density formula for the law of time spent on the positive side of one-dimensional diffusion processes. J. Math. Kyoto Univ. 45 (2005), no. 4, 781--806. doi:10.1215/kjm/1250281657. https://projecteuclid.org/euclid.kjm/1250281657


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