Electronic Communications in Probability

A note on a.s. finiteness of perpetual integral functionals of difusions

Davar Khoshnevisan, Paavo Salminen, and Marc Yor

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Abstract

In this note we use the boundary classification of diffusions in order to derive a criterion for the convergence of perpetual integral functionals of transient real-valued diffusions. We present a second approach, based on Khas'minskii's lemma, which is applicable also to spectrally negative L'evy processes. In the particular case of transient Bessel processes, our criterion agrees with the one obtained via Jeulin's convergence lemma.

Article information

Source
Electron. Commun. Probab., Volume 11 (2006), paper no. 11, 108-117.

Dates
Accepted: 6 July 2006
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465058854

Digital Object Identifier
doi:10.1214/ECP.v11-1203

Mathematical Reviews number (MathSciNet)
MR2231738

Zentralblatt MATH identifier
1111.60061

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

Keywords
Brownian motion random time change exit boundary local time additive functional stochastic differential equation Khas'minskii's lemma spectrally negative L'evy process

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Khoshnevisan, Davar; Salminen, Paavo; Yor, Marc. A note on a.s. finiteness of perpetual integral functionals of difusions. Electron. Commun. Probab. 11 (2006), paper no. 11, 108--117. doi:10.1214/ECP.v11-1203. https://projecteuclid.org/euclid.ecp/1465058854


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