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Harnack Inequality and Hölder Regularity Estimates for a Lévy Process with Small Jumps of High Intensity

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  • Ante Mimica

    (Universität Bielefeld)

Abstract

We consider a Lévy process in ℝ d (d≥3) with the characteristic exponent $$\varPhi(\xi)=\frac{|\xi|^2}{\ln(1+|\xi|^2)}-1.$$ The scale invariant Harnack inequality and a priori estimates of harmonic functions in Hölder spaces are proved.

Suggested Citation

  • Ante Mimica, 2013. "Harnack Inequality and Hölder Regularity Estimates for a Lévy Process with Small Jumps of High Intensity," Journal of Theoretical Probability, Springer, vol. 26(2), pages 329-348, June.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:2:d:10.1007_s10959-011-0361-8
    DOI: 10.1007/s10959-011-0361-8
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    References listed on IDEAS

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    1. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
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