The Symbol Associated with the Solution of a Stochastic Differential Equation
Probability
2012-05-07 v3
Abstract
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.
Keywords
Cite
@article{arxiv.0912.1458,
title = {The Symbol Associated with the Solution of a Stochastic Differential Equation},
author = {Rene L. Schilling and Alexander Schnurr},
journal= {arXiv preprint arXiv:0912.1458},
year = {2012}
}
Comments
21 pages