On Harnack inequality for α-stable Ornstein-Uhlenbeck processes

Mathematische Zeitschrift

Volumn 258, Issue 3, 2008, Pages 609-628

  Jakubowski, Tomasz ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

stable Ornstein Uhlenbeck process; Harmonic functions; Harnack inequality

Indexed keywords

EID: 38149087634     PISSN: 00255874     EISSN: 14321823     Source Type: Journal    
DOI: 10.1007/s00209-007-0188-2     Document Type: Article

References (14)

1. Bass R.F., Levin D.A. (2002). Harnack inequalities for jump processes. Potential Anal. 17(4): 375-388
2. Blumenthal, R.M., Getoor, R.K.: Markov processes and potential theory. vol. 29, Pure and Applied Mathematics, Academic, New York (1968)
3. Bogdan K., Byczkowski T. (1999). Probabilistic proof of boundary Harnack principle for α-harmonic functions. Potential Anal. 11(2): 135-156
4. Bogdan K., Stós A., Sztonyk P. (2003). Harnack inequality for stable processes on d-sets. Studia Math. 158(2): 163-198
5. Chen Z.-Q., Fitzsimmons P.J., Takeda M., Ying J., Zhang T.-S. (2004). Absolute continuity of symmetric Markov processes. Ann. Probab. 32(3A): 2067-2098
6. Chen Z.-Q., Kumagai T. (2003). Heat kernel estimates for stable-like processes on d-sets. Stoch. Process. Appl. 108(1): 27-62
7. Chen Z.-Q., Song R. (2003). Drift transforms and Green function estimates for discontinuous processes. J. Funct. Anal. 201(1): 262-281
8. Chung K.L., Zhao Z.X. (1995). From Brownian motion to Schrödinger's equation, vol. 312, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, Berlin
9. Hebisch W., Saloff-Coste L. (2001). On the relation between elliptic and parabolic Harnack inequalities. Ann. Inst. Fourier (Grenoble) 51(5): 1437-1481
10. Ikeda N., Watanabe S. (1962). 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
11. Jakubowski, T.: The estimates of the mean first exit time from a ball for the α-stable Ornstein-Uhlenbeck processes. Stoch. Process. Appl. (to appear)
12. Janicki A., Weron A. (1994). Simulation and chaotic behavior of α-stable stochastic processes, vol. 178, Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, New York
13. Samorodnitsky, G., Taqqu, M.S.: Stable non-Gaussian random processes (Stochastic models with infinite variance). Stochastic Modeling. Chapman & Hall, New York (1994)
14. Song R., Vondraček Z. (2004). Harnack inequality for some classes of Markov processes. Math. Z. 246(1-2): 177-202