The Symbol Associated with the Solution of a Stochastic Differential Equation

Rene L. Schilling, Alexander Schnurr

Published 2009-12-08, updated 2010-12-01Version 3

We consider a stochastic differential equations which is driven by a Levy process. It turns out that the solution process is a Feller process if the coefficient of the SDE is bounded. Using a probabilistic formula we calculate the symbol, which appears in the Fourier representation of the generator, explicitely. Using the symbol we introduce indices which are generalizations of the well known Blumenthal-Getoor index. These indices are then used to obtain some fine properties of the solution process.