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.
Citation
Rene Schilling. Alexander Schnurr. "The Symbol Associated with the Solution of a Stochastic Differential Equation." Electron. J. Probab. 15 1369 - 1393, 2010. https://doi.org/10.1214/EJP.v15-807
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