A LEVY-TYPE CHARACTERIZATION OF ONE-DIMENSIONAL DIFFUSIONS

Authors
VOIT M
Citation
M. Voit, A LEVY-TYPE CHARACTERIZATION OF ONE-DIMENSIONAL DIFFUSIONS, Archiv der Mathematik, 70(3), 1998, pp. 235-238
Citations number
6
Categorie Soggetti
Mathematics,Mathematics
Journal title
Archiv der Mathematik → ACNP
ISSN journal
0003889X
Volume
70
Issue
3
Year of publication
1998
Pages
235 - 238
Database
ISI
SICI code
0003-889X(1998)70:3<235:ALCOOD>2.0.ZU;2-D
Abstract
We present a Levy-type characterization for time-homogeneous diffusion processes on R of the following kind: A continuous process X = (X-t)( t greater than or equal to 0) on R is a diffusion belonging to a secon d-order differential operator L if and only if the two processes (p(X- t))(t greater than or equal to 0) and (s(X-t)-t)(t greater than or equ al to 0) are local martingales where the functions p, s are suitable s olutions of Lp = 0 and Ls = 1.