Electronic Journal of Probability
- Electron. J. Probab.
- Volume 15 (2010), paper no. 43, 1369-1393.
The Symbol Associated with the Solution of a Stochastic Differential Equation
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.
Electron. J. Probab., Volume 15 (2010), paper no. 43, 1369-1393.
Accepted: 18 September 2010
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J75: Jump processes
Secondary: 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx] 60H20: Stochastic integral equations 60J25: Continuous-time Markov processes on general state spaces 60G51: Processes with independent increments; Lévy processes 60G17: Sample path properties
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Schilling, Rene; Schnurr, Alexander. The Symbol Associated with the Solution of a Stochastic Differential Equation. Electron. J. Probab. 15 (2010), paper no. 43, 1369--1393. doi:10.1214/EJP.v15-807. https://projecteuclid.org/euclid.ejp/1464819828