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On the parabolic generator of a general one-dimensional Lévy process

   
@article{ECP1366,
	author = {Nathalie Eisenbaum and Andreas Kyprianou},
	title = {On the parabolic generator of a general one-dimensional Lévy process},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {Stochastic   calculus , local time-space, It^o formula, parabolic generator.},
	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.},
	pages = {no. 20, 198-209},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1366},    
        url = {http://ecp.ejpecp.org/article/view/1366}}