TY - JOUR

T1 - On the parabolic generator of a general one-dimensional Levy process

AU - Eisenbaum, N

AU - Kyprianou, A E

N1 - ID number: ISI:000255073600003

PY - 2008/4/9

Y1 - 2008/4/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=42449157741&partnerID=8YFLogxK

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

M3 - Article

VL - 13

SP - 198

EP - 209

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

ER -