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hĥ-transforms of positivity preserving semigroups and associated Markov processes

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Abstract

The hĥ--transforms of positivity preserving semigroups and their associated Markov processes are investigated in this paper. In particular, it is shown that any quasi-regular positivity preserving coercive form is hĥ--associated with a pair of special standard processes which are in weak duality.

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References

  1. Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin, 1994

    Book  MATH  Google Scholar 

  2. Ma, Z. M., Röckner, M.: Introduction to the Theory of (Non-symmetric) Dirichlet Forms, Springer-Verlag, Berlin-Heidelberg-New York, 1992

    MATH  Google Scholar 

  3. Chen, Z. Q., Fukushima, M.: Symmetric Markov Processes, Time Change and Boundary Theory, Princeton University Press, to appear

  4. Ma, Z. M., Sun, W.: Some topics on Dirichlet forms. In: New Trend in Stochastic Analysis and Related Topics, a Volume in Honour of Professor K. D. Elworthy, 2010, to appear

  5. Ma, Z. M., Röckner, M.: Markov processes associated with positivity preserving coercive forms. Canad. J. Math., 47, 817–840 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hu, Z. C., Ma, Z. M., Sun, W.: Extensions of Lévy-Khintchine formula and Beurling-Deny formula in semi-Dirichlet forms setting. J. Funct. Anal., 239, 179–213 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Blumenthal, R. M., Getoor, R. K.: Markov Processes and Potential Theory, Academic Press, New York, 1968

    MATH  Google Scholar 

  8. Chung, K. L., Walsh, J. B.: Markov Processes, Brownian Motion, and Time Symmetry, Springer, Berlin, 2005

    MATH  Google Scholar 

  9. Fukushima, M.: Almost polar sets and an ergodic theorem. J. Math. Soc. Japan, 26, 17–32 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chen, Z. Q., Fukushima, M., Ying, J. G.: Entrance law, exit system and Lévy system of time-changed processes. Illinois J. Math., 50, 269–312 (2006)

    MathSciNet  MATH  Google Scholar 

  11. Bergh, J., Löfström, J.: Interpolation Spaces, an Introduction, Springer-Verlag, Berlin-Heidelberg-New York, 1976

    MATH  Google Scholar 

  12. Ma, L., Sun, W.: On the generalized Feynman-Kac transformation for nearly symmetric Markov processes. J. Theoret. Probab., DOI: 10.1007/s10959-010-0318-3

  13. Kuwae, K.: Maximum principles for subharmonic functions via local semi-Dirichlet forms. Canad. J. Math., 60, 822–874 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Fitzsimmons, P. J.: On the quasi-regularity of semi-Dirichlet forms. Potential Anal., 15, 158–185 (2001)

    Article  MathSciNet  Google Scholar 

  15. Chen, Z. Q., Fitzsimmons, P. J., Kuwae, K., et al.: Perturbation of symmetric Markov processes. Probab. Theory Related Fields, 140, 239–275 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Science and Computing Technology, Central South University, Changsha, 410083, P. R. China

    Xin Fang Han

  2. Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Xin Fang Han & Zhi-Ming Ma

  3. Department of Mathematics and Statistics, Concordia University, Montreal, H3G1M8, Canada

    Wei Sun

Authors
  1. Xin Fang Han
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  2. Zhi-Ming Ma
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  3. Wei Sun
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Correspondence to Xin Fang Han.

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Dedicated to Professor Hua Loo-keng on his 100th birth anniversary

Supported by NSFC (Grant No. 10961012), 973 Project, Key Lab of CAS (Grant No. 2008DP173182), and NSERC (Grant No. 311945-2008)

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Han, X.F., Ma, ZM. & Sun, W. hĥ-transforms of positivity preserving semigroups and associated Markov processes. Acta. Math. Sin.-English Ser. 27, 369–376 (2011). https://doi.org/10.1007/s10114-011-0597-3

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  • DOI: https://doi.org/10.1007/s10114-011-0597-3

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