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Moderate deviations for the quenched mean of the super-Brownian motion with random immigration

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Abstract

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration are proved for 3 ⩽ d ⩽ 6, which fills in the gap between central limit theorem (CLT) and large deviation principle (LDP).

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References

  1. Hong W M, Li Z H. A central limit theorem for the super-Brownian motion with super-Brownian immigration. J Appl Probab, 36: 1218–1224 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  2. Dawson D A, Gorostiza L G, Li Z H. Non-local branching superprocesses and some related models. Acta Appl Math, 74: 93–112 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Hong W M. Large deviations for the super-Brownian motion with super-Brownian immigration. J Theoret Probab, 16(4): 899–922 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Hong W M, Zeitouni O. A quenched CLT for super-Brownian motion with random immigration. J Theoret Probab, 2007 20(4): 807–820 (2007)

    Article  MathSciNet  Google Scholar 

  5. Hong W M. Quenched mean limit theorems for the super-Brownian motion with super-Brownian immigration. Infin Dimens Anal, Quantum Probab Relat Top, 8(3): 383–396 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dawson D A. Measure-valued Markov processes, In: Lect Notes Math, Vol. 1541, Berlin: Springer-Verlag, 1993, 1–260

    Google Scholar 

  7. Perkins E A. Dawson-Watanabe superprocesses and measure-valued diffusions. In: Lecture Notes Math, Vol. 1781, Berlin: Springer-Verlag, 2002, 132–318

    Google Scholar 

  8. Iscoe I. A weighted occupation time for a class of measure-valued critical branching Brownian motion. Probab Theory Related Fields, 71: 85–116 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dynkin E B. Superprocesses and their linear additive functionals. Trans Amer Math Soc, 314: 255–282 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  10. Wang Z K. Power series expansion for superprocesses. Math Acta Scientia (in Chinese), 10: 361–364 (1990)

    Google Scholar 

  11. Dawson D A. The critical measure diffusion process. Z Wahrsch Verw Geb, 40: 125–145 (1977)

    Article  MATH  Google Scholar 

  12. Widder D V. The Laplace Transform. Princeton: Princeton University Press, 1941

    MATH  Google Scholar 

  13. Dembo A, Zeitouni O. Large Deviations Techniques and Applications, Berlin: Springer, 1998

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, 100875, China

    Hong WenMing

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  1. Hong WenMing
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Correspondence to Hong WenMing.

Additional information

This work was supported by the Program for New Century Excellent Talents in University (Grant No. 05-0143) and the National Natural Science Foundation of China (Grant No. 10721091)

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Hong, W. Moderate deviations for the quenched mean of the super-Brownian motion with random immigration. Sci. China Ser. A-Math. 51, 343–350 (2008). https://doi.org/10.1007/s11425-007-0190-5

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  • DOI: https://doi.org/10.1007/s11425-007-0190-5

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