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


Reference:

Eisenbaum, N. and Kyprianou, A. E., 2008. On the parabolic generator of a general one-dimensional Levy process. Electronic Communications in Probability, 13, pp. 198-209.

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http://www.math.washington.edu/~ejpecp/ECP/viewarticle.php?id=1991&layout=abstract

Abstract

The purpose of this note is twofold. Firstly to complete a recent accumulation of results concerning extended version of Itô's formula for any one dimensional Lévy processes, X. Secondly, we use the latter to characterise the parabolic generator of X A := {(f, g) : f(X., ·) - ∫0 g(Xs, s)ds is a local martingale}. 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.

Details

Item Type Articles
CreatorsEisenbaum, N.and Kyprianou, A. E.
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code6933
Additional InformationID number: ISI:000255073600003

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