Symmetric stable processes on unbounded domains

Potential Analysis

Volumn 25, Issue 4, 2006, Pages 371-386

  Siudeja, Bartłomiej ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Exit time; Heat kernel; Horn shaped domains; Symmetric stable process

Indexed keywords

EID: 33751061422     PISSN: 09262601     EISSN: 1572929X     Source Type: Journal    
DOI: 10.1007/s11118-006-9022-4     Document Type: Article

References (16)

1. Bafluelos, R., van den Berg, M.; Dirichlet eigenfunctions for horn-shaped regions and Laplacians on cross sections. J. London Math. Soc. (2) 53(3), 503-511 (1996)
2. Bafluelos, R., Bogdan, K.: Symmetric stable processes in cones. Potential Anal. 21(3), 263-288 (2004)
3. Bafluelos, R., Bogdan, K.: Symmetric stable processes in parabola-shaped regions. Proc. Amer. Math. Soc. 133, 3581-3587 (2005).
4. Bafluelos, R., Smits, R.G.: Brownian motion in cones. Probab. Theory Related Fields 108(3), 299-319 (1997)
5. Blumenthal, R.M., Getoor, R.K.: Some theorems on stable processes. Trans. Amer. Math. Soc. 95, 263-273 (1960)
6. Burkholder, D.L.: Exit times of Brownian motion, harmonic majorization, and Hardy spaces. Adv. Math. 26(2), 182-205 (1977)
7. Ikeda, N., Watanabe, S.: On some relations between the harmonic measure and the Levy measure for certain class of Markov processes. J. Math. Kyoto Univ. 2, 79-95 (1962)
8. Jakubowski, T.: The estimates for the Green function in Lipschitz domains for the symmetric stable processes. Probab. Math. Stat. 22(2), Acta Univ. Wratislav. No. 2470, 419-441 (2002)
9. John, F.: Extremum Problems with Inequalities as Subsidiary Conditions, Courant Anniversary Volume, pp. 187-204. Interscience, New York (1948)
10. Kulczycki, T.: Exit time and Green function of cone for symmetric stable processes. Probab. Math. Stat. 19(2), Acta Univ. Wratislav. No. 2198, 227-374 (1999)
11. Kulczycki, T.: Intrinsic ultracontractivity for symmetric stable processes. Bull. Pol. Acad. Sci., Math. 46(3), 325-334 (1998)
12. Kulczycki, T.: Properties of Green function of symmetric stable processes. Probab. Math. Stat. 17(2), Acta Univ. Wratislav. No. 2029, 339-364 (1997)
13. Kulczycki, T., Siudeja, B.: Intrinsic ultracontractivity of Feynman-Kac semigroup for relativistic stable processes. Trans. Amer. Math. Soc., posted on June 13, 2006, PII S 0002-9947(06)03931-6 (to appear in print)
14. Landkof, N.S.: Foundations of modern potential theory. Translated from the Russian by A. P. Doohovskoy. Die Grundlehren der mathematischen Wissenschaften, Band 180. Springer-Verlag, New York Heidelberg, (1972)
15. n of symmetric stable processes. Ill. J. Math. 46(1), 155-163 (2002)
16. Méndez-Hernández, P.J.: Exit times of symmetric stable processes from unbounded convex domains, preprint.