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2006 A note on a.s. finiteness of perpetual integral functionals of difusions
Davar Khoshnevisan, Paavo Salminen, Marc Yor
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Electron. Commun. Probab. 11: 108-117 (2006). DOI: 10.1214/ECP.v11-1203


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.


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Davar Khoshnevisan. Paavo Salminen. Marc Yor. "A note on a.s. finiteness of perpetual integral functionals of difusions." Electron. Commun. Probab. 11 108 - 117, 2006.


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

zbMATH: 1111.60061
MathSciNet: MR2231738
Digital Object Identifier: 10.1214/ECP.v11-1203

Primary: 60J65
Secondary: 60J60

Keywords: additive functional , Brownian motion , exit boundary , Khas'minskii's lemma , Local time , Random time change , spectrally negative L'evy process , Stochastic differential equation

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