Multilevel Multitype Branching Models of an Information System

  • D. A. Dawson
  • Y. Wu
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 84)


We describe a class of multilevel multitype branching particle systems and indicate how it can be applied to model a dynamical information system.

AMS(MOS) subject classifications. Primary 60K35, Secondary 68B15.

Key words

Dynamical information system multilevel multitype branching multilevel measure-valued process 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    References Athreya, K.B. and Ney, P.E. (1977). Branching Processes. Springer-Verlag, BerlinHeidelberg-New York.Google Scholar
  2. [2]
    Bhattacharya, Rabi N. and Waymire, Edward C.(1990). Stochastic processes with applications. Wiley, New York.Google Scholar
  3. [3]
    Dawson, D. and Hochberg, K. (1991). A multilevel branching model. Adv. Appl. Prob., 23, 701–715.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    D.A. Dawson (1993). Measure-valued Markov Processes in Ecole d’Eté de Probabilités de Saint-Flour XXI, Lect. Notes in Math. 1541, 1–260, Springer-Verlag.Google Scholar
  5. [5]
    Dawson, D.A., Hochberg, K.J. and V. Vinogradov (1994). On path properties of super-2 processes I. in Measure-Valued Processes, Stochastic Partial Differential Equations, and Interacting Systems, ed. D.A. Dawson, 69–82, CRM-AMS.Google Scholar
  6. [6]
    Dawson, D.A., Hochberg, K.J. and V. Vinogradov (1994). On path properties of super-2 processes II. in M. Pinsky, ed., Proceedings of the 1993 AMS Summer Res. Institute Vol. 57, 385–404, Amer. Math. Soc.Google Scholar
  7. [7]
    Dawson, D.A., Hochberg, K.J. and Wu, Y. (1990). Multilevel branching systems. White Noise Analysis, World Scientific Publ.Google Scholar
  8. [8]
    Dawson, D.A. and Ivanoff, B.G. (1978). Branching diffusions and random measures. In Branching Processes, ed. A. Joffe and P. Ney, 61–104, Dekker, New York.Google Scholar
  9. [9]
    D.A. Dawson and Y. Wu (1994) Simulation of hierarchically structured information systems. preprint.Google Scholar
  10. [10]
    L.G. Gorostiza (1994) Asymptotic fluctuations and critical dimension for a two-level branching system, preprint.Google Scholar
  11. [11]
    Gorostiza, L.G., Hochberg, K.J. and Wakolbinger, A.. Persistence of a critical super-2 process. J. Appl. Prob., in press.Google Scholar
  12. [12]
    Harris, T.E.(1963). The Theory of Branching Processes. Springer, Berlin.zbMATHCrossRefGoogle Scholar
  13. [13]
    K.J. Hochberg (1993) Hierarchically structured branching populations with spatial motion, Rocky Mountain J. Math., to appear.Google Scholar
  14. [14]
    E.A. Perkins (1992). Measure-valued branching diffusions with spatial interactions, Prob. Theor. Rel. Fields 94, 189–245.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    Wu, Y. (1991). Dynamic particle systems and multilevel measure branching processes, Ph.D. thesis. Carleton University.Google Scholar
  16. [16]
    Wu, Y. (1993). A multilevel birth-death particle system and its continuous diffusion. Adv. Appl. Prob., Vol. 25, No. 3, 549–569.zbMATHCrossRefGoogle Scholar
  17. [17]
    Wu, Y. (1993). Multilevel particle systems and measure-valued processes. Preprint.Google Scholar
  18. [18]
    Wu, Y. (1994). Asymptotic behavior of the two level measure branching process. Ann. of Prob., 22, No. 2, to appear.Google Scholar
  19. [19]
    Y. Wu (1994) A three level particle system and existence of general multilevel measure-valued processes in “Measure-valued Processes, Stochastic Partial Differential Equations, and Interacting Systems” CRM Proceedin gs and Lecture Notes 5, 233–241, Amer. Math. Soc.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • D. A. Dawson
    • 1
  • Y. Wu
    • 1
  1. 1.Department of Mathematics and StatisticsCarleton UniversityOttawaCanada

Personalised recommendations