Symmetric stable processes in parabola-shaped regions

Proceedings of the American Mathematical Society

Volumn 133, Issue 12, 2005, Pages 3581-3587

  Bañuelos, Rodrigo ^a   Bogdan, Krzysztof ^b,c  

^a PURDUE UNIVERSITY   (United States)

^b INSTITUTE OF MATHEMATICS   (Poland)

^c WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Exit time; Harmonic measure; Parabola; Symmetric stable process

Indexed keywords

EID: 29144473279     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-05-07923-2     Document Type: Article

References (17)

1. R. Bañuelos and K. Bogdan, Symmetric stable processes in cones, Potential Analysis, 21 (2004), 263-288. MR2075671
2. R. Bañuelos and T. Carroll, Sharp Integrability for Brownian Motion in Parabola-shaped Regions (2003), J. Funct. Anal. 218 (2005), 219-253. MR2101220.
3. R. Bañuelos, R. D. DeBlassie and R. Smits, The first exit time of planar Brownian motion from the interior of a parabola, Ann. Prob. 29 (2001), 882-901. MR1849181 (2002h:60165)
4. R. Bañuelos and R. Smits, Brownian motion in cones, Prob. Th. Rel. Fields, 108 (1997), 299-319. MR1465162 (98k:60065)
5. M. van den Berg, Subexponential behavior of the Dirichlet heat kernel, J. Funct. Anal. 198 (2003), 28-42. MR1962352 (2003m:60211)
6. R. M. Blumenthal, R. K. Getoor and D.B. Ray, On the distribution of first hits for the symmetric stable process, Trans. Amer. Math. Soc. 99 (1961), 540-554. MR0126885 (23:A4179)
7. K. Bogdan and T. Jakubowski, Problème de Dirichlet pour les fonctions α-harmoniques sur les domaines coniques (2004), preprint.
8. K. Bogdan and T. Żak, On Kelvin transformation, to appear in J. Theoretical Probability.
9. K. Burdzy and T. Kulczycki, Stable processes have thorns, Ann. Probab. 31 (2003), 170-194. MR1959790 (2003k:60079)
10. D. L. Burkholder, Exit times of Brownian motion, harmonic majorization, and Hardy spaces, Advances in Math. 26(2) (1977), 182-205. MR0474525 (57:14163)
11. R. D. DeBlassie and R. Smits. Brownian motion in twisted domains, Transactions of the American Mathematical Society 357 (2005), 1245-1274. MR2110439
12. R. DeBlassie, The first exit time of a two-dimensional symmetric stable process from a wedge, Ann. Prob. 18 (1990), 1034-1070. MR1062058 (91j:60078)
13. T. Kulczycki, Exit time and Green function of cone for symmetric stable processes, Probab. Math. Statist. 19(2) (1999), 337-374. MR1750907 (2001f:60077)
14. W. Li, The first exit time of Brownian motion from unbounded convex domains, Annals of Probability 31 (2003), 1078-1096. MR1964959 (2004c:60126)
15. M. Lifshitz and Z. Shi, The first exit time of Brownian motion from parabolic domain, Bernoulli 8(6) (2002), 745-767. MR1963660 (2004d:60213)
16. n of symmetric stable processes Illinois J. Math. 46 (2002), 155-163. MR1936081 (2003i:60070)
17. K.-I. Sato, Lévy Processes and Infinitely Divisible Distributions, University Press Springer-Verlag, Cambridge, 1999. MR1739520 (2003b:60064)