Harnack inequality and H\" older regularity estimates for a L\' evy process with small jumps of high intensity

Details Harnack inequality and H\" older regularity estimates for a L\' evy process with small jumps of high intensity Harnack inequality and H\" older regularity estimates for a L\' evy process with small jumps of high intensity

2011-04-24

arxiv.org/abs/1104.4610v2

Mathematics

Probability

20 pages

Scientific paper

We consider a L\' evy process in $\R^d$ $ (d\geq 3)$ with the characteristic
exponent \[ \Phi(\xi)=\frac{|\xi|^2}{\ln(1+|\xi|^2)}-1. \] The scale invariant
Harnack inequality and apriori estimates of harmonic functions in H\" older
spaces are proved.

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