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On the weak convergence of super-Brownian motion with immigration

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Abstract

We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting processes are Gaussian processes.

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References

  1. 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 

  2. Hong W M. Longtime behavior for the occupation time of super-Brownian motion with random immigration. Stochastic Process Appl, 102: 43–62: (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Hong W M. Functional central limit theorem for super α-stable processes. Sci China Ser A, 47(6): 874–881: (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bojdecki T, Gorostiza L G, Talarczyk A. Limit theorems for occupation time fluctuations of branching systems I. Long-range dependence. Stochastic Process Appl, 116: 1–18: (2006)

    MATH  MathSciNet  Google Scholar 

  5. Bojdecki T, Gorostiza L G, Talarczyk A. Limit theorems for occupation time fluctuations of branching systems II. Critical and large dimensions. Stochastic Process Appl, 116: 19–35: (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bojdecki T, Gorostiza L G, Talarczyk A. Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems. Electron Comm Probab, 12: 161–172: (2006)

    MathSciNet  Google Scholar 

  7. Bojdecki T, Gorostiza L G, Talarczyk A. A long range dependence stable process and an infinite branching system. Ann Probab, 35(2): 500–527: (2007)

    Article  MathSciNet  Google Scholar 

  8. Bojdecki T, Gorostiza L G, Talarczyk A. Occupation time fluctuations of an infinite-variance branching system in large dimensions. Bernoulli, 13: 20–39: (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Zhang M. Functional central limit theorem for the super-Brownian motion with super-Brownian immigration. J Theoret Probab, 18(3): 665–685: (2005)

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  11. Mitoma I. Tightness of probabilities on C([0,1],−) and D([0,1],−’). Ann Probab, 11: 989–999: (1983)

    Article  MATH  MathSciNet  Google Scholar 

  12. 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 

  13. Ethier S N, Kurtz T G. Markov Processes: Characterization and Convergence. New York: Wiley, 1986

    MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Mei Zhang

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  1. Mei Zhang
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Correspondence to Mei Zhang.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10721091)

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Zhang, M. On the weak convergence of super-Brownian motion with immigration. Sci. China Ser. A-Math. 52, 1875–1886 (2009). https://doi.org/10.1007/s11425-009-0110-y

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  • DOI: https://doi.org/10.1007/s11425-009-0110-y

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