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
SN - 1083-589X
VL - 13
SP - 198
EP - 209
JO - Electronic Communications in Probability
JF - Electronic Communications in Probability
ER -