α-Continuity properties of the symmetric α-stable process

Transactions of the American Mathematical Society

Volumn 359, Issue 5, 2007, Pages 2343-2359

  Deblassie, R Dante ^a   Méndez Hernández, Pedro J ^b,c  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY OF UTAH   (United States)

^c UNIVERSIDAD DE COSTA RICA   (Costa Rica)

Author keywords

Eigenfunctions; Eigenvalues; Symmetric stable process

Indexed keywords

EID: 34547341496     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-06-04032-3     Document Type: Article

References (22)

1. R.A. Adams, L.I. Hedberg (1984). Inclusion relations among fine topologies in nonlinear potential theory, Indiana Univ. Math. J. 33 117-126. MR0726108 (85c:31011)
2. D. Aldous (1978). Stopping times and tightness, Annals of Probability 6 335-340. MR0474446 (57:14086)
3. R.F. Bass (1988). Uniqueness in law for pure jump processes, Probability Theory and Related Fields 79 271-287. MR0958291 (89h:60118)
4. R.F. Bass and D.A. Levin (2002). Harnack inequalities for jump processes, Potential Analysis 17 375-388. MR1918242 (2003e:60194)
5. R. Banuelos and T. Kulczycki (2004). The Cauchy process and the Steklov problem, J. Funct. Anal. 211 355-423. MR2056835 (2005b:60124) (Pubitemid 38773471)
6. R. Banuelos, R. Latala, and P. Mendez-Hernandez (2001). A Brascamp-Lieb-Luttinger-type inequality and applications to symmetric stable processes, Proc. Amer. Math. Soc. 129 2997-3008. MR1840105 (2002c:60125) (Pubitemid 33334210)
7. P. Billingsley (1968). Convergence of Probability Measures, Wiley, New York. MR0233396 (38:1718)
8. R.M. Blumenthal and R.K. Getoor (1959). The asymptotic distribution of the eigenvalues for a class of Markov operators, Pacific J. Math. 9 399-408. MR0107298 (21:6023)
9. R.M. Blumenthal and R.K. Getoor (1960). Some theorems on stable processes, Trans. Amer. Math. Soc. 95 263-273. MR0119247 (22:10013)
10. K. Bogdan (1997). The boundary Harnack principle for the fractional Laplacian, Studia Mathematica 123 43-80. MR1438304 (98g:31005) (Pubitemid 127339541)
11. Z.-Q. Chen and R. Song (2005). Two-sided eigenvalue estimates for subordinate processes in domains, J. Funct. Anal. 226 (2005), 90-113. MR2158176 (2006d:60116) (Pubitemid 41102502)
12. E.B. Davies (1995). Spectral Theory and Differential Operators, Cambridge Univ. Press, Cambridge. MR1349825 (96h:47056)
13. R.D. DeBlassie (1993). The first exit time of a two-dimensional symmetric stable process from a wedge, Annals of Probability 18 134-170. MR1062058 (91j:60078)
14. R.D. DeBlassie (2004). Higher order PDE's and symmetric stable processes, Probability Theory and Related Fields 129 495-536. MR2078980 (2005d:60079) (Pubitemid 39056960)
15. R.D. DeBlassie (2005). Correction to "Higher order PDE's and symmetric stable processes, " Probab. Theory Related Fields 133 141-143. MR2197141
16. S.N. Ethier and T.G. Kurtz (1986). Markov Processes, Wiley, New York. MR0838085 (88a:60130)
17. M. Fukushima, Y. Oshima, and M. Takeda (1994). Dirichlet Forms and Symmetric Markov Processes, de Gruyter Studies in Mathematics 19 Walter de Gruyter, Berlin. MR1303354 (96f:60126)
18. N. Ikeda and S. Watanabe (1962). On some relations between the harmonic measure and the Levy measure for a certain class of Markov processes, J. Math. Kyoto Univ. 2 79-95. MR0142153 (25:5546)
19. N of symmetric stable processes, Illinois Journal of Mathematics 46 155-163. MR1936081 (2003i:60070) (Pubitemid 36161155)
20. P.J. Mendez-Hernandez (2002). Brascamp-Lieb-Luttinger inequalities for convex domains of finite inradius, Duke Math. J. 13 93-131. MR1905393 (2003b:31005)
21. K. Sato, Levy Processes and Infinitely Divisible Distributions, Cambribge University Press, Cambridge, 1990. MR1739520 (2003b:60064)
22. E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1970. MR0290095 (44:7280)