Science in China Series A: Mathematics

, Volume 47, Issue 6, pp 874–881 | Cite as

Functional central limit theorem for super α-stable processes



A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (0 < α ≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d < 2α, the limiting process is Brownian motion.


super α-stable processes occupation time central limit theorem evolution equation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dawson, D. A., The critical measure diffusion process, Z. Wahrsch. Verw. Geb., 1977, 40: 125–145.MATHCrossRefGoogle Scholar
  2. 2.
    Hong, W. M., Longtime behavior for the occupation time of super-Brownian motion with random immigration, Stochastic Process, 2002, 102: 43–62.MATHCrossRefGoogle Scholar
  3. 3.
    Hong, W. M., Large deviations for super-Brownian motion with super-Brownian immigration, J. Theoret. Probab., 2003, 16: 899–922.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Hong, W. M., Li, Z. H., A central limit theorem for the super-Brownian motion with super-Brownian immigration, J. Appl. Probab., 1999, 36: 1218–1224.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Iscoe, I., A weighted occupation time for a class of measure-valued critical branching Brownian motion, Probab. Th. Rel. Fields, 1986, 71: 85–116.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Iscoe, I., Ergodic theory and a local occupation time for measure-valued critical branching Brownian motion, Stochastics, 1986, 18: 197–243.MATHMathSciNetGoogle Scholar
  7. 7.
    Dawson, D. A., Gorostiza, L. G., Wakolbinger, A., Occupation time fluctuations in branching systems, J. Theoret. Probab., 2001, 14: 729–796.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Quastel, J., Jankowski, H., Sheriff, J., Central limit theorem for zero-range processes, Methods Appl. Anal., 2002, 9: 393–406.MATHMathSciNetGoogle Scholar
  9. 9.
    Zöhle, I., Functional central limit theorem for branching random walks, Workshop on Spatially Distributed and Hierarchically Structured Stochastic Systems, Montreal, 2002.Google Scholar
  10. 10.
    Dawson, D. A., Measure-valued Markov processes, in Lect. Notes Math., Berlin: Springer-Verlag, 1993, 1541: 1–260.Google Scholar
  11. 11.
    Samorodnitsky, G., Taqqu, M. S., Stable non-Gaussian random processes, New York: Chapman and Hall, 1994.MATHGoogle Scholar

Copyright information

© Science in China Press 2004

Authors and Affiliations

  1. 1.Department of MathematicsBeijing Normal UniversityBeijingChina

Personalised recommendations