Open Access
2008 On the parabolic generator of a general one-dimensional Lévy process
Nathalie Eisenbaum, Andreas Kyprianou
Author Affiliations +
Electron. Commun. Probab. 13: 198-209 (2008). DOI: 10.1214/ECP.v13-1366


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.


Download Citation

Nathalie Eisenbaum. Andreas Kyprianou. "On the parabolic generator of a general one-dimensional Lévy process." Electron. Commun. Probab. 13 198 - 209, 2008.


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

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

Keywords: Itô formula , local time-space , parabolic generator , stochastic calculus

Back to Top