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 Electronic Journal of Probability > Vol. 15(2010) > Paper 43 open journal systems 


The Symbol Associated with the Solution of a Stochastic Differential Equation

Rene L. Schilling, TU Dresden
Alexander Schnurr, TU Dortmund


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.


Full text: PDF

Pages: 1369-1393

Published on: September 18, 2010
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Electronic Journal of Probability. ISSN: 1083-6489