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On the parabolic generator of a general one-dimensional Lévy process
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Nathalie Eisenbaum, CNRS
Andreas Kyprianou, University of Bath
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Abstract
The purpose of this note is twofold. Firstly to complete a recent accumulation of results concerning extended version of Ito's formula for any one dimensional Lévy processes, $X$.
Secondly, we use the latter to characterise the parabolic generator of $X$,
[
{bf A}:= left{
(f,g) : f(X_cdot,cdot) - int_0^cdot g(X_s, s)ds text{ is a local martingale}
right}.
]
We also establish a necessary condition for a pair of functions to be in the domain of the parabolic generator when $X$ has a Gaussian component.
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Full text: PDF
Pages: 198-209
Published on: April 9, 2008
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Electronic Communications in Probability. ISSN: 1083-589X |
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