@article{EJP80,
author = {Arindam Sengupta and Anish Sarkar},
title = {Finitely Polynomially Determined Lévy Processes},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {6},
year = {2000},
keywords = {Lévy process, additive process, Lévy's characterisation, Lévy measure, Kolmogorov measure.},
abstract = {A time-space harmonic polynomial for a continuous-time process $X=\{X_t : t \ge 0\} $ is a two-variable polynomial $ P $ such that $ \{ P(t,X_t) : t \ge 0 \} $ is a martingale for the natural filtration of $ X $. Motivated by Lévy's characterisation of Brownian motion and Watanabe's characterisation of the Poisson process, we look for classes of processes with reasonably general path properties in which a characterisation of those members whose laws are determined by a finite number of such polynomials is available. We exhibit two classes of processes, the first containing the Lévy processes, and the second a more general class of additive processes, with this property and describe the respective characterisations.},
pages = {no. 7, 1-22},
issn = {1083-6489},
doi = {10.1214/EJP.v6-80},
url = {http://ejp.ejpecp.org/article/view/80}}