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A localization formula in Dirichlet form theory
Authors:
Zhen-Qing Chen and Masatoshi Fukushima
Journal:
Proc. Amer. Math. Soc. 140 (2012), 1815-1822
MSC (2010):
Primary 60J25, 31C25; Secondary 60J45, 60J50
Posted:
September 12, 2011
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Additional Information
Abstract: A localization energy formula is established for symmetric Markov processes on Luzin spaces.
References
Bibliography
- 1.
Z.-Q. Chen and M. Fukushima, Symmetric Markov Processes, Time Change, and Boundary Theory. Princeton University Press, to appear.
- 2.
Zhen-Qing
Chen, Masatoshi
Fukushima, and Jiangang
Ying, Traces of symmetric Markov processes and their
characterizations, Ann. Probab. 34 (2006),
no. 3, 1052–1102. MR 2243879
(2008a:60194), http://dx.doi.org/10.1214/009117905000000657
- 3.
Zhen
Qing Chen, Zhi
Ming Ma, and Michael
Röckner, Quasi-homeomorphisms of Dirichlet forms, Nagoya
Math. J. 136 (1994), 1–15. MR 1309378
(95m:31020)
- 4.
Masatoshi
Fukushima, Yōichi
Ōshima, and Masayoshi
Takeda, Dirichlet forms and symmetric Markov processes, de
Gruyter Studies in Mathematics, vol. 19, Walter de Gruyter & Co.,
Berlin, 1994. MR
1303354 (96f:60126)
- 5.
Sheng
Wu He, Jia
Gang Wang, and Jia
An Yan, Semimartingale theory and stochastic calculus, Kexue
Chubanshe (Science Press), Beijing, 1992. MR 1219534
(95d:60080)
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Additional Information
Zhen-Qing Chen
Affiliation:
Department of Mathematics, University of Washington, Seattle, Washington 98195
Email:
zqchen@uw.edu
Masatoshi Fukushima
Affiliation:
Branch of Mathematical Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email:
fuku2@mx5.canvas.ne.jp
DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-11036-0
PII:
S 0002-9939(2011)11036-0
Keywords:
Symmetric Markov process,
Hunt process,
Dirichlet form,
extended Dirichlet space,
energy measure,
additive functional,
martingale additive functional
Received by editor(s):
December 15, 2010
Received by editor(s) in revised form:
January 26, 2011
Posted:
September 12, 2011
Additional Notes:
The first author’s research was partially supported by NSF Grants DMS-0906743 and DMR-1035196.
The second author’s research was supported by Grant-in-Aid for Scientific Research of MEXT No. 19540125
Communicated by:
Richard C. Bradley
Article copyright:
© Copyright 2011 Zhen-Qing Chen and Masatoshi Fukushima
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