|
On notions of harmonicity
Author(s):
Zhen-Qing
Chen
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3497-3510.
MSC (2000):
Primary 60J45, 31C05;
Secondary 31C25, 60J25
Posted:
May 28, 2009
MathSciNet review:
2515419
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we address the equivalence of the analytic and probabilistic notions of harmonicity in the context of general symmetric Hunt processes on locally compact separable metric spaces. Extensions to general symmetric right processes on Lusin spaces, including infinite dimensional spaces, are mentioned at the end of this paper.
References:
-
- 1.
- M. T. Barlow, R. F. Bass, T. Kumagai and A. Teplyaev, Uniqueness of Brownian motion on Sierpinski carpets. Preprint, 2008.
- 2.
- R. F. Bass, M. Kassmann and T. Kumagai, private communications, 2007.
- 3.
- A. Benveniste and J. Jacod, Systèmes de Lévy des processus de Markov. Invent. Math. 21 (1973), 183-198. MR 0343375 (49:8117)
- 4.
- Z.-Q. Chen and M. Fukushima, Symmetric Markov Processes, Time Change and Boundary Theory. Book manuscript, 2009.
- 5.
- Z.-Q. Chen and T. Kumagai, Heat kernel estimates for stable-like processes on
 -sets. Stochastic Process Appl. 108 (2003), 27-62. MR 2008600 (2005d:60135) - 6.
- Z.-Q. Chen and T. Kumagai, A priori Hölder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps. To appear in Rev. Mat. Iberoamericana.
- 7.
- Z.-Q. Chen, Z.-M. Ma and M. Röckner, Quasi-homeomorphisms of Dirichlet forms, Nagoya Math. J. 136 (1994) 1-15. MR 1309378 (95m:31020)
- 8.
- K. L. Chung, Greenian bounds for Markov processes. Potential Analysis 1 (1992), 83-92. MR 1245226 (95d:60125)
- 9.
- M. Fukushima, Y. Ōshima and M. Takeda, Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin-New York, 1994. MR 1303354 (96f:60126)
- 10.
- M. L. Silverstein, Symmetric Markov Processes. Lecture Notes in Math., 426, Springer-Verlag, Berlin-New York, 1974. MR 0386032 (52:6891)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
60J45, 31C05,
31C25, 60J25
Retrieve articles in all Journals with
MSC (2000):
60J45, 31C05,
31C25, 60J25
Additional Information:
Zhen-Qing
Chen
Affiliation:
Department of Mathematics, University of Washington, Seattle, Washington 98195
Email:
zchen@math.washington.edu
DOI:
10.1090/S0002-9939-09-09945-6
PII:
S 0002-9939(09)09945-6
Keywords:
Harmonic function,
uniformly integrable martingale,
symmetric Hunt process,
Dirichlet form,
L\'evy system
Received by editor(s):
October 25, 2008,
Received by editor(s) in revised form:
February 16, 2009
Posted:
May 28, 2009
Additional Notes:
The research of this author is supported in part by NSF Grant DMS-0600206.
Communicated by:
Edward C. Waymire
Copyright of article:
Copyright
2009,
Zhen-Qing Chen
|
