The Symbol Associated with the Solution of a Stochastic Differential Equation

Rene Schilling; Alexander Schnurr

doi:10.1214/EJP.v15-807

2010 The Symbol Associated with the Solution of a Stochastic Differential Equation

Rene Schilling, Alexander Schnurr

Author Affiliations +

Electron. J. Probab. 15: 1369-1393 (2010). DOI: 10.1214/EJP.v15-807

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.

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Rene Schilling and Alexander Schnurr "The Symbol Associated with the Solution of a Stochastic Differential Equation," Electronic Journal of Probability 15(none), 1369-1393, (2010). https://doi.org/10.1214/EJP.v15-807

Accepted: 18 September 2010; Published: 2010

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