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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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

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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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