The Symbol Associated with the Solution of a Stochastic Differential Equation

Rene L. Schilling; Alexander Schnurr

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arXiv · 0912.1458

The Symbol Associated with the Solution of a Stochastic Differential Equation

Rene L. Schilling·Alexander Schnurr

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Abstract

We consider a stochastic differential equations which is driven by a Levy process. It turns out that the solution process is a Feller process if the coefficient of the SDE is bounded. Using a probabilistic formula we calculate the symbol, which appears in the Fourier representation of the generator, explicitely. Using the symbol we introduce indices which are generalizations of the well known Blumenthal-Getoor index. These indices are then used to obtain some fine properties of the solution process.

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Rene L. Schilling, Alexander Schnurr. 2009-12-08. The Symbol Associated with the Solution of a Stochastic Differential Equation. https://arxiv.org/abs/0912.1458

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