Harnack inequalities for some Lévy processes

Potential Analysis

Volumn 32, Issue 3, 2010, Pages 275-303

  Mimica, Ante ^a  

^a UNIVERSITY OF ZAGREB   (Croatia)

Author keywords

Green function; Harmonic function; Harnack inequality; Poisson kernel; Random walk; Stable process; Subordinate Brownian motion; Subordinator

Indexed keywords

EID: 77950410247     PISSN: 09262601     EISSN: 1572929X     Source Type: Journal    
DOI: 10.1007/s11118-009-9153-5     Document Type: Article

References (23)

1. Bass, R. F., Kassmann, M.: Harnack inequalities for non-local operators of variable order. Trans. Am. Math. Soc. 357, 837-850 (2005).
2. d with unbounded range. Trans. Am. Math. Soc. 360, 2041-2075 (2008).
3. Bass, R. F., Levin, D. A.: Harnack inequalities for jump processes. Potential Anal. 17, 375-388 (2002).
4. Bertoin, J.: Lévy Processes. Cambridge University Press, Cambridge (1996).
5. Bingham, N. H., Goldie, C. M., Teugels, J. L.: Regular Variation. Cambridge University Press, Cambridge (1987).
6. Bogdan, K., Sztonyk, P.: Potential theory for Lévy stable processes. Bull. Pol. Acad. Sci., Math. 50, 361-372 (2002).
7. Bogdan, K., Sztonyk, P.: Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian. Stud. Math. 181, 101-123 (2007).
8. Bogdan, K., Sztonyk, P.: Harnack's inequality for stable Lévy processes. Potential Anal. 22, 133-150 (2005).
9. Chen, Z.-Q., Song, R.: Estimates on green functions and poisson kernels of symmetric stable processes. Math. Ann. 312, 465-601 (1998).
10. Chen, Z.-Q., Kim, P., Kumagai, T.: Weighted Poincaré inequality and heat kernel estimates for finite range jump processes. Math. Ann. 342, 833-883 (2008).
11. Chung, K. L., Zhao, Z.: From Brownian Motion to Schrödinger's Equation. Springer, Berlin (2001).
12. Delmotte, T.: Parabolic Harnack inequality and estimates of Markov chains on graphs. Rev. Mat. Iberoam. 15, 181-232 (1999).
13. Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet Forms and Symmetric Markov Processes. Walter De Gruyter, Berlin (1994).
14. Grigor'yan, A., Telcs, A.: Harnack inequalities and sub-Gaussian estimates for random walks. Math. Ann. 324, 521-556 (2002).
15. Ikeda, N., Watanabe, S.: On some relations between the harmonic measure and the Lévy measure for a certain class of Markov processes. Math. J. Kyoto Univ. 2, 79-95 (1962).
16. Jacob, N.: Pseudo Differential Operators and Markov Processes, vol. 1. Imperial College Press, London (2001).
17. Kim, P., Song, R.: Potential theory of truncated stable processes. Math. Z. 256, 139-173 (2007).
18. Kim, P., Song, R., Vondraček, Z.: Boundary Harnack principle for subordinate Brownian motions. Stoch. Process. Appl. 119, 1601-1631 (2009).
19. Lawler, G. F., Polaski, T. W.: Harnack inequalities and difference estimates for random walks with infinite range. J. Theor. Probab. 6, 781-802 (1993).
20. Sato, K.-I.: Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1999).
21. Song, R., Vondraček, Z.: Harnack inequalities for some classes of Markov processes. Math. Z. 246, 177-202 (2004).
22. Song, R., Vondraček, Z.: Potential theory of subordinate Brownian motion. In: Graczyk, P., Stos, A. (eds.) Potential Analysis of Stable Processes and its Extensions. Lecture Notes in Mathematics, vol. 1980, pp. 87-176. Springer, New York (2009).
23. Sztonyk, P.: On harmonic measure for Lévy processes. Probab. Math. Stat. 20, 383-390 (2000).