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Subordinating the killed process versus killing the subordinate process

Author(s): Ping He; Jiangang Ying
Journal: Proc. Amer. Math. Soc. 135 (2007), 523-529.
MSC (2000): Primary 60J45
Posted: August 1, 2006
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Abstract: In this paper we shall prove that the process obtained by killing first and subordinating next is a subprocess of the process obtained by subordinating first and killing next.

References:

1.: Chen, Z.-Q., Song, R., Two-sided eigenvalue estimates for subordinate processes in domain, to appear in J. Funct. Anal.
2.: Fukushima, M., Oshima, Y. and Takeda, M., DIRICHLET FORMS AND SYMMETRIC MARKOV PROCESSES, DE GRUYTER, BERLIN, 1994 MR 1303354 (96F:60126)
3.: OKURA, H., RECURRENCE AND TRANSIENCE CRITERIA FOR SUBORDINATED MARKOV PROCESSES, FORUM MATH., 14(2002), 121-146 MR 1880197 (2002M:60146)
4.: SHARPE, M.J., GENERAL THEORY OF MARKOV PROCESSES, ACADEMIC PRESS, 1988 MR 0958914 (89M:60169)
5.: SILVERSTEIN, M., SYMMETRIC MARKOV PROCESSES, LECTURE NOTES IN MATH, SPRINGER, 1974 MR 0386032 (52:6891)
6.: YING, J., KILLING AND SUBORDINATION, PROC. AMER. MATH. SOC., 124, NO. 7(1996), 2215-2222 MR 1346994 (97A:31005)
7.: YING, J., CHARACTERIZATION OF BIVARIATE REVUZ MEASURES, KYUSHU J. MATH., 51, NO.1(1997), 185-193 MR 1437316 (98F:60148)

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Additional Information:

Ping He
Affiliation: Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, People's Republic of China
Email: pinghe@mail.shufe.edu.cn

Jiangang Ying
Affiliation: Institute of Mathematics, Fudan University, Shanghai, People's Republic of China
Email: jgying@fudan.edu.cn

DOI: 10.1090/S0002-9939-06-08471-1
PII: S 0002-9939(06)08471-1
Keywords: Dirichlet forms, subprocesses, subordinate
Received by editor(s): April 12, 2005
Received by editor(s) in revised form: August 18, 2005
Posted: August 1, 2006
Additional Notes: The research of the second author was supported in part by funding from NSFC No. 10271109
Communicated by: Richard Bradley
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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Ping He, Jiangang Ying, Subordinating the killed process verus killing the subordinate process, Proceedings of the American Mathematical Society 135 (2007), 523--529.


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