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2010 The Symbol Associated with the Solution of a Stochastic Differential Equation
Rene Schilling, Alexander Schnurr
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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. 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

Information

Accepted: 18 September 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60116
MathSciNet: MR2721050
Digital Object Identifier: 10.1214/EJP.v15-807

Subjects:
Primary: 60J75
Secondary: 47G30, 60G17, 60G51, 60H20, 60J25

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Vol.15 • 2010
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