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2008 On the parabolic generator of a general one-dimensional Lévy process
Nathalie Eisenbaum, Andreas Kyprianou
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Electron. Commun. Probab. 13(none): 198-209 (2008). DOI: 10.1214/ECP.v13-1366

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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Nathalie Eisenbaum. Andreas Kyprianou. "On the parabolic generator of a general one-dimensional Lévy process." Electron. Commun. Probab. 13 198 - 209, 2008. https://doi.org/10.1214/ECP.v13-1366

Information

Accepted: 9 April 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1191.60063
MathSciNet: MR2399282
Digital Object Identifier: 10.1214/ECP.v13-1366

Subjects:
Primary: 60G44
Secondary: 60H05, 60J55, 60J65

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