Stable processes have thorns

Annals of Probability

Volumn 31, Issue 1, 2003, Pages 170-194

  Burdzy, Krzysztof ^a   Kulczycki, Tadeusz ^b,c  

^a UNIVERSITY OF WASHINGTON   (United States)

^b INSTITUTE OF MATHEMATICS   (Poland)

^c WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Local properties of trajectories; Symmetric stable process; Thorn points; Thorns

Indexed keywords

EID: 0037253515     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1046294308     Document Type: Article

References (19)

1. ADELMAN, O., BURDZY, K. and PEMANTLE, R. (1998). Sets avoided by Brownian motion. Ann. Probab. 26 429-464.
2. BASS, R. and BURDZY, K. (1999). Cutting Brownian Paths. Amer. Math. Soc., Providence, RI.
3. BERTOIN, J. (1996). Lévy Processes. Cambridge Univ. Press.
4. BLUMENTHAL, R. M. and GETOOR, R. K. (1968). Markov Processes and Potential Theory. Academic Press, New York.
5. BLUMENTHAL, R. M., GETOOR, R. K. and RAY, D. B. (1961). On the distribution of first hits for the symmetric stable processes. Trans. Amer. Math. Soc. 99 540-554.
6. BOGDAN, K. (1999). Representation of α-harmonic functions in Lipschitz domains. Hiroshima Math. J. 29 227-243.
7. BOGDAN, K., BURDZY, K. and CHEN, Z.-Q. Censored stable processes. Preprint.
8. BOGDAN, K. and BYCZKOWSKI, T. (1999). Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains. Studia Math. 133 53-92.
9. BOGDAN, K. and BYCZKOWSKI, T. (1999). Probabilistic proof of boundary Harnack principle for α-harmonic functions. Potential Anal. 11 135-156.
10. BURDZY, K. (1985). Brownian paths and cones. Ann. Probab. 13 1006-1010.
11. CHEN, Z.-Q. (1999). Multidimensional symmetric stable processes. Korean J. Comput. Appl. Math. 6 227-266.
12. DAVIS, B. (1983). On Brownian slow points. Z. Wahrsch. Verw. Gebiete 64 359-367.
13. DVORETZKY, A. (1963). On the oscillation of the Brownian motion process. Israel J. Math. 1 212-214.
14. EVANS, S. N. (1985). On the Hausdorff dimension of Brownian cone points. Math. Proc. Cambridge Philos. Soc. 98 343-353.
15. GREENWOOD, P. and PERKINS, E. (1983). A conditioned limit theorem for random walk and Brownian local time on square root boundaries. Ann. Probab. 11 227-261.
16. IKEDA, N. and 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.
17. JAFFARD, S. (1999). The multifractal nature of Levy processes. Probab. Theory Related Fields 114 207-227.
18. LE GALL, J.-F. (1987). Mouvement brownien, cônes et processus stables. Probab. Theory Related Fields 76 587-627.
19. SHIMURA, M. (1985). Excursions in a cone for two-dimensional Brownian motion. J. Math. Kyoto Univ. 25 433-443.