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

1. Bass, R.F., Kassmann, M.: Harnack inequalities for non-local operators of variable order. Trans. Am. Math. Soc. 357, 837–850 (2005)

   Article  MathSciNet  MATH  Google Scholar 

2. Bass, R.F., Kassmann, M.: Hölder continuity of harmonic functions with respect to operators of variable order. Commun. Partial Differ. Equ. 30, 1249–1259 (2005)

   Article  MathSciNet  MATH  Google Scholar 

3. Bass, R.F., Levin, D.: Harnack inequalities for jump processes. Potential Anal. 17, 375–388 (2002)

   Article  MathSciNet  MATH  Google Scholar 

4. Bertoin, J.: Lévy Processes. Cambridge University Press, Cambridge (1996)

   MATH  Google Scholar 

5. Bingham, N.H., Goldie, C.M., Teugels, J.L.: Regular Variation. Cambridge University Press, Cambridge (1987)

   MATH  Google Scholar 

6. Bogdan, K., Sztonyk, P.: Harnack’s inequality for stable Lévy processes. Potential Anal. 22, 133–150 (2005)

   Article  MathSciNet  MATH  Google Scholar 

7. Chen, Z.-Q., Kumagai, T.: Heat kernel estimates for stable-like processes on d-sets. Stoch. Process. Appl. 108(1), 27–62 (2003)

   Article  MathSciNet  MATH  Google Scholar 

8. Chung, K.L., Zhao, Z.: From Brownian motion to Schrödinger equation. Springer, Berlin (2001)

   MATH  Google Scholar 

9. Ikeda, N., Watanabe, S.: On some relations between the harmonic measure and the Lévy measure for a certain class of Markov processes. J. Math. Kyoto Univ. 2, 79–95 (1962)

   MathSciNet  MATH  Google Scholar 

10. Kassmann, M.: Harnack inequalities and Hölder regularity estimates for nonlocal operators revisited, preprint (2010)

11. Kim, P., Song, R.: Potential theory of truncated stable processes. Math. Z. 256, 139–173 (2007)

    Article  MathSciNet  MATH  Google Scholar 

12. Kim, P., Song, R., Vondraček, Z.: Two-sided Green function estimates for killed subordinate Brownian motions, preprint (2010)

13. Mimica, A.: Harnack inequalities for some Lévy processes. Potential Anal. 32, 275–303 (2010)

    Article  MathSciNet  MATH  Google Scholar 

14. Rao, M., Song, R., Vondraček, Z.: Green function estimates and Harnack inequality for subordinate Brownian motions. Potential Anal. 25, 1–27 (2006)

    Article  MathSciNet  Google Scholar 

15. Sato, K.-I.: Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

16. Schilling, R.L., Song, R., Vondraček, Z.: Bernstein functions: theory and applications. Walter de Gruyter, Berlin (2010)

    MATH  Google Scholar 

17. Šikić, H., Song, R., Vondraček, Z.: Potential theory of geometric stable processes. Probab. Theory Relat. Fields 135, 547–575 (2006)

    Article  MATH  Google Scholar 

18. Song, R., Vondraček, Z.: Harnack inequalities for some classes of Markov processes. Math. Z. 246, 177–202 (2004)

    Article  MathSciNet  MATH  Google Scholar 

19. Sztonyk, P.: On harmonic measure for Lévy processes. Probab. Math. Stat. 20, 383–390 (2000)

    MathSciNet  MATH  Google Scholar 

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