A note on a.s. finiteness of perpetual integral functionals of
difusions
Davar Khoshnevisan, University of Utah, Utah, U.S.A.
Paavo Salminen, AAbo Akademi University, AAbo, Finland
Marc Yor, Universit'e Pierre et Marie Curie, Paris, France
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.
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