Sharp bounds for green functions and jumping functions of subordinate killed brownian motions in bounded C1,1 domains

Electronic Communications in Probability

Volumn 9, Issue , 2004, Pages 96-105

  Song, Renming ^a   Vondracek, Zoran ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b UNIVERSITY OF ZAGREB   (Croatia)

Author keywords

Dirichlet form; Green function; Jumping function; Killed Brownian motion; Subordinator

Indexed keywords

EID: 5644262638     PISSN: None     EISSN: 1083589X     Source Type: Journal    
DOI: 10.1214/ECP.v9-1114     Document Type: Article

References (14)

1. J. Bertoin. Levy Processes. Cambridge University Press, Cambridge, 1996.
2. Z.-Q. Chen. Gaugeability and conditional gaugeability. Trans. Amer. Math. Soc. 354 (2002), 4639-4679
3. Z.-Q. Chen and R. Song. General gauge and conditional gauge theorems. Ann. Probab. 30 (2002), 1313-1339.
4. Z.-Q. Chen and R. Song. Conditional gauge theorem for non-local Feynman-Kac transforms. Probab. Theory Rel. Fields 125 (2003), 45-72.
5. E. B. Davies. Heat kernels and spectral theory. Cambridge University Press, Cambridge, 1989.
6. M. Fukushima, Y. Oshima and M. Takeda. Dirichlet forms and symmetric Markov processes. Walter De Gruyter, Berlin, 1994.
7. J. Glover, M. Rao, H. Sikic and R. Song. T-potentials. in Classical and modern potential theory and applications (Chateau de Bonas, 1993). 217-232, Kluwer Acad. Publ., Dordrecht, 1994.
8. N. Jacob. Pseudo Differential Operators and Markov Processes. Vol. 1, Imperial College Press, London, 2001.
9. K. Okura. Recurrence and transience criteria for subordinated symmetric Markov processes. Forum Math. 14 (2002), 121-146.
10. M. Rao, R. Song and Z. Vondracek. Green function estimates and Harnack inequality for subordinate Brownian motions. Preprint, 2004.
11. R. Song. Sharp bounds on the density, Green function and jumping function of subordinate killed BM. Probab. Theory Rel. Fields 128 (2004), 606-628.
12. R. Song and Z. Vondracek. Potential theory of subordinate killed Brownian motion in a domain. Probab. Theory Rel. Fields 125 (2003), 578-592.
13. R. Song and Z. Vondracek. Potential theory of special subordinators and subordinate killed stable processes. Preprint, 2004
14. Q. S. Zhang. The boundary behavior of heat kernels of Dirichlet Laplacians. J. Differential Equations 182 (2002), 416-430.