Electronic Communications in Probability

Sharp Bounds for Green and Jumping Functions of Subordinate Killed Brownian Motions

Renming Song and Zoran Vondracek

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Abstract

In this paper we obtain sharp bounds for the Green function and jumping function of a subordinate killed Brownian motion in a bounded $C^{1,1}$ domain, where the subordinating process is a subordinator whose Laplace exponent has certain asymptotic behavior at infinity.

Article information

Source
Electron. Commun. Probab., Volume 9 (2004), paper no. 11, 96-105.

Dates
Accepted: 6 October 2004
First available in Project Euclid: 26 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1464286691

Digital Object Identifier
doi:10.1214/ECP.v9-1114

Mathematical Reviews number (MathSciNet)
MR2108856

Zentralblatt MATH identifier
1060.60078

Subjects
Primary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]
Secondary: 60J75: Jump processes

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Song, Renming; Vondracek, Zoran. Sharp Bounds for Green and Jumping Functions of Subordinate Killed Brownian Motions. Electron. Commun. Probab. 9 (2004), paper no. 11, 96--105. doi:10.1214/ECP.v9-1114. https://projecteuclid.org/euclid.ecp/1464286691


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References

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