@article{EJP807,
author = {Rene Schilling and Alexander Schnurr},
title = {The Symbol Associated with the Solution of a Stochastic Differential Equation},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {15},
year = {2010},
keywords = {stochastic differential equation; L'evy process; semimartingale; pseudo-differential operator; Blumenthal-Getoor index; sample path properties},
abstract = {We consider stochastic differential equations which are driven by multidimensional Levy processes. We show that the infinitesimal generator of the solution is a pseudo-differential operator whose symbol is calculated explicitely. For a large class of Feller processes many properties of the sample paths can be derived by analysing the symbol. It turns out that the solution of the SDE under consideration is a Feller process if the coefficient of the SDE is bounded and that the symbol is of a particulary nice structure.},
pages = {no. 43, 1369-1393},
issn = {1083-6489},
doi = {10.1214/EJP.v15-807},
url = {http://ejp.ejpecp.org/article/view/807}}